Assignment 2
Nicole Hayek
2022-9-08
Problem 2
Carefully explain the differences between the KNN classifier and KNN regression methods.
The difference is KNN classifier is used when the response variable is categorical (qualitative), while KNN regressor is used when the variable is quanitiative.
Problem 9
Produce a scatterplot matrix which includes all of the variables in the data set Produce a scatterplot matrix which includes all of the variables in the data set.
Compute the matrix of correlations between the variables using the function cor(). You will need to exclude the name variable, cor() which is qualitative.
Use the lm() function to perform a multiple linear regression with mpg as the response and all other variables except name as the predictors. Use the summary() function to print the results.
Comment on the output. For instance:
Is there a relationship between the predictors and the response?
Which predictors appear to have a statistically significant relationship to the response?
What does the coefficient for the year variable suggest?
Use the plot() function to produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers? Does the leverage plot identify any observations with unusually high leverage?
Use the * and : symbols to fit linear regression models with interaction effects. Do any interactions appear to be statistically significant?
Try a few different transformations of the variables, such as log(X), ???X, X2. Comment on your findings.
#b)
Auto <- read.csv("~/Desktop/ALL CSV FILES - 2nd Edition/Auto.csv")
Auto1<-Auto
Auto1$name=NULL#c)
y1<-lm(mpg~ .-name,data=Auto)
summary(y1)##
## Call:
## lm(formula = mpg ~ . - name, data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.174 -1.155 0.000 1.136 11.972
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.507e+01 4.483e+00 -3.362 0.000876 ***
## cylinders 3.452e-02 4.169e-01 0.083 0.934063
## displacement 2.486e-03 9.220e-03 0.270 0.787621
## horsepower100 -4.762e+00 1.535e+00 -3.103 0.002101 **
## horsepower102 -6.148e+00 3.150e+00 -1.952 0.051928 .
## horsepower103 -8.564e+00 3.117e+00 -2.747 0.006377 **
## horsepower105 -3.704e+00 1.606e+00 -2.306 0.021782 *
## horsepower107 -4.898e+00 3.143e+00 -1.558 0.120241
## horsepower108 -9.591e+00 3.200e+00 -2.997 0.002957 **
## horsepower110 -5.434e+00 1.531e+00 -3.550 0.000448 ***
## horsepower112 -7.162e+00 2.105e+00 -3.402 0.000761 ***
## horsepower113 -2.841e-01 3.138e+00 -0.091 0.927923
## horsepower115 -4.009e+00 1.845e+00 -2.173 0.030537 *
## horsepower116 -7.607e+00 3.231e+00 -2.354 0.019217 *
## horsepower120 -7.447e+00 2.075e+00 -3.588 0.000389 ***
## horsepower122 -7.411e+00 3.224e+00 -2.298 0.022240 *
## horsepower125 -6.323e+00 2.236e+00 -2.828 0.005006 **
## horsepower129 -1.026e+01 2.593e+00 -3.957 9.49e-05 ***
## horsepower130 -6.508e+00 2.117e+00 -3.074 0.002308 **
## horsepower132 1.668e-01 3.256e+00 0.051 0.959183
## horsepower133 -1.046e+01 3.200e+00 -3.268 0.001210 **
## horsepower135 -6.698e+00 3.257e+00 -2.056 0.040644 *
## horsepower137 -5.868e+00 3.309e+00 -1.773 0.077238 .
## horsepower138 -8.446e+00 3.332e+00 -2.535 0.011760 *
## horsepower139 -7.534e+00 2.607e+00 -2.890 0.004137 **
## horsepower140 -4.686e+00 2.064e+00 -2.271 0.023882 *
## horsepower142 -8.786e+00 3.318e+00 -2.648 0.008521 **
## horsepower145 -6.833e+00 2.074e+00 -3.294 0.001108 **
## horsepower148 -5.172e+00 3.437e+00 -1.505 0.133499
## horsepower149 -5.670e+00 3.349e+00 -1.693 0.091469 .
## horsepower150 -5.798e+00 1.908e+00 -3.039 0.002585 **
## horsepower152 -7.340e+00 3.377e+00 -2.174 0.030528 *
## horsepower153 -4.807e+00 2.725e+00 -1.764 0.078742 .
## horsepower155 -5.326e+00 2.725e+00 -1.955 0.051575 .
## horsepower158 -6.045e+00 3.407e+00 -1.774 0.077012 .
## horsepower160 -6.464e+00 2.792e+00 -2.315 0.021273 *
## horsepower165 -5.881e+00 2.277e+00 -2.583 0.010274 *
## horsepower167 -5.090e+00 3.569e+00 -1.426 0.154863
## horsepower170 -5.107e+00 2.390e+00 -2.136 0.033457 *
## horsepower175 -5.188e+00 2.397e+00 -2.164 0.031226 *
## horsepower180 -6.699e+00 2.360e+00 -2.839 0.004844 **
## horsepower190 -5.777e+00 2.629e+00 -2.198 0.028740 *
## horsepower193 -4.992e+00 3.375e+00 -1.479 0.140241
## horsepower198 -4.049e+00 3.042e+00 -1.331 0.184238
## horsepower200 -6.263e+00 3.374e+00 -1.856 0.064389 .
## horsepower208 -6.903e+00 3.622e+00 -1.906 0.057644 .
## horsepower210 -5.620e+00 3.411e+00 -1.648 0.100492
## horsepower215 -5.094e+00 2.745e+00 -1.856 0.064511 .
## horsepower220 -4.131e+00 3.721e+00 -1.110 0.267788
## horsepower225 -6.011e+00 2.845e+00 -2.113 0.035438 *
## horsepower230 -4.335e+00 3.559e+00 -1.218 0.224108
## horsepower46 -7.356e-01 2.455e+00 -0.300 0.764612
## horsepower48 1.262e+01 2.172e+00 5.807 1.63e-08 ***
## horsepower49 8.643e-01 3.135e+00 0.276 0.782980
## horsepower52 3.069e+00 1.988e+00 1.544 0.123649
## horsepower53 8.689e-01 2.422e+00 0.359 0.720074
## horsepower54 -1.984e+00 3.189e+00 -0.622 0.534270
## horsepower58 3.679e+00 2.406e+00 1.529 0.127351
## horsepower60 3.227e-01 1.841e+00 0.175 0.860977
## horsepower61 2.169e+00 3.140e+00 0.691 0.490208
## horsepower62 -9.257e-01 2.387e+00 -0.388 0.698421
## horsepower63 2.667e+00 2.075e+00 1.285 0.199647
## horsepower64 5.764e+00 3.113e+00 1.851 0.065103 .
## horsepower65 2.848e+00 1.608e+00 1.771 0.077506 .
## horsepower66 4.209e+00 3.104e+00 1.356 0.176176
## horsepower67 9.597e-01 1.544e+00 0.622 0.534688
## horsepower68 -1.494e+00 1.754e+00 -0.852 0.395172
## horsepower69 3.245e+00 2.084e+00 1.557 0.120614
## horsepower70 1.497e+00 1.511e+00 0.991 0.322532
## horsepower71 -1.592e+00 1.787e+00 -0.891 0.373891
## horsepower72 -3.836e+00 1.737e+00 -2.208 0.028015 *
## horsepower74 -3.521e-01 2.083e+00 -0.169 0.865897
## horsepower75 -1.927e+00 1.491e+00 -1.292 0.197340
## horsepower76 2.414e+00 1.904e+00 1.268 0.205821
## horsepower77 -4.900e-01 3.146e+00 -0.156 0.876312
## horsepower78 -1.867e+00 1.710e+00 -1.092 0.275692
## horsepower79 -2.164e+00 2.368e+00 -0.914 0.361547
## horsepower80 4.924e-01 1.657e+00 0.297 0.766607
## horsepower81 -2.859e+00 2.363e+00 -1.210 0.227371
## horsepower82 1.088e+00 3.107e+00 0.350 0.726334
## horsepower83 -3.161e-01 1.893e+00 -0.167 0.867455
## horsepower84 -1.767e+00 1.758e+00 -1.005 0.315482
## horsepower85 -3.681e+00 1.594e+00 -2.309 0.021605 *
## horsepower86 -2.825e+00 1.799e+00 -1.571 0.117312
## horsepower87 -1.806e-01 2.413e+00 -0.075 0.940380
## horsepower88 -2.736e+00 1.434e+00 -1.909 0.057281 .
## horsepower89 -1.589e+00 3.107e+00 -0.511 0.609446
## horsepower90 -2.680e+00 1.431e+00 -1.873 0.061994 .
## horsepower91 -6.656e+00 3.125e+00 -2.130 0.033999 *
## horsepower92 -2.559e+00 1.734e+00 -1.476 0.140999
## horsepower93 -3.149e+00 3.127e+00 -1.007 0.314790
## horsepower94 -6.246e+00 3.129e+00 -1.996 0.046811 *
## horsepower95 -3.789e+00 1.523e+00 -2.487 0.013435 *
## horsepower96 -3.612e+00 2.109e+00 -1.713 0.087848 .
## horsepower97 -6.301e+00 1.644e+00 -3.834 0.000154 ***
## horsepower98 -4.792e+00 2.410e+00 -1.989 0.047665 *
## weight -4.043e-03 7.107e-04 -5.688 3.08e-08 ***
## acceleration -2.356e-01 1.066e-01 -2.211 0.027822 *
## year 7.164e-01 5.192e-02 13.798 < 2e-16 ***
## origin 1.373e+00 3.103e-01 4.426 1.35e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.815 on 297 degrees of freedom
## Multiple R-squared: 0.903, Adjusted R-squared: 0.8706
## F-statistic: 27.92 on 99 and 297 DF, p-value: < 2.2e-16# i) There is a relationship between at least one predictor and the response variable shown by a p-value of less than 0.05 for the f statistic meaning we can reject the null hypothesis.
# ii) Displacement, weight, year and origin have a statistically significant relationship with mpg shown be their p-values.
# iii) The coefficient of year variable is significant and positive which suggests that if all other variables are constant than on average mpg increases by 0.75 every year.
#d)
par(mfrow=c(2,2))
plot(y1)## Warning: not plotting observations with leverage one:
## 7, 24, 28, 29, 68, 89, 105, 111, 114, 117, 118, 120, 124, 146, 151, 160, 191, 208, 211, 233, 237, 246, 275, 278, 288, 289, 291, 298, 334, 345, 362, 397## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
plot(predict(y1),rstudent(y1))
plot(hatvalues(y1))
which.max(hatvalues(y1))## 7
## 7## 14#e)
y2<-lm(mpg~.:.,Auto1)
summary(y2)##
## Call:
## lm(formula = mpg ~ .:., data = Auto1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5941 -0.1449 0.0000 0.0616 6.0550
##
## Coefficients: (371 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.438e+01 1.542e+02 0.158 0.87466
## cylinders 1.723e+01 2.322e+01 0.742 0.45978
## displacement -6.631e-01 5.624e-01 -1.179 0.24131
## horsepower100 5.188e+00 1.103e+02 0.047 0.96257
## horsepower102 4.878e+00 1.069e+01 0.456 0.64926
## horsepower103 -1.338e+01 1.118e+01 -1.197 0.23417
## horsepower105 1.336e+01 1.087e+02 0.123 0.90239
## horsepower107 -1.558e+01 1.527e+01 -1.021 0.31005
## horsepower108 -2.806e+01 1.509e+01 -1.860 0.06595 .
## horsepower110 8.079e+00 1.097e+02 0.074 0.94144
## horsepower112 3.662e+01 1.897e+02 0.193 0.84730
## horsepower113 9.789e+00 1.734e+01 0.565 0.57372
## horsepower115 -3.441e+02 4.583e+02 -0.751 0.45465
## horsepower116 -1.729e+01 1.423e+01 -1.215 0.22735
## horsepower120 -3.166e+01 5.687e+01 -0.557 0.57898
## horsepower122 -2.300e+01 1.525e+01 -1.508 0.13480
## horsepower125 -3.619e+01 2.639e+01 -1.371 0.17347
## horsepower129 -8.259e+01 1.040e+02 -0.794 0.42923
## horsepower130 -1.922e+02 2.513e+02 -0.765 0.44629
## horsepower132 -7.480e+00 1.694e+01 -0.441 0.65986
## horsepower133 -1.870e+01 2.120e+01 -0.882 0.38011
## horsepower135 8.390e+00 1.175e+01 0.714 0.47680
## horsepower137 9.056e+00 1.239e+01 0.731 0.46643
## horsepower138 1.361e+01 1.979e+01 0.688 0.49319
## horsepower139 -8.403e+01 1.220e+02 -0.689 0.49280
## horsepower140 -5.996e+01 1.404e+02 -0.427 0.67035
## horsepower142 1.405e+01 1.755e+01 0.801 0.42524
## horsepower145 -1.095e+01 1.547e+02 -0.071 0.94371
## horsepower148 2.524e+01 1.681e+01 1.502 0.13640
## horsepower149 2.062e+01 1.573e+01 1.311 0.19306
## horsepower150 -6.253e+01 1.172e+02 -0.533 0.59495
## horsepower152 1.809e+01 1.743e+01 1.038 0.30199
## horsepower153 -1.346e+02 6.190e+02 -0.217 0.82831
## horsepower155 -2.439e+01 2.628e+02 -0.093 0.92625
## horsepower158 1.999e+01 1.624e+01 1.231 0.22147
## horsepower160 -4.774e+02 1.001e+03 -0.477 0.63433
## horsepower165 -3.251e+02 9.086e+02 -0.358 0.72130
## horsepower167 3.244e+01 2.478e+01 1.309 0.19378
## horsepower170 -1.607e+02 2.833e+02 -0.567 0.57183
## horsepower175 -4.179e+01 3.129e+02 -0.134 0.89401
## horsepower180 -1.388e+02 1.329e+02 -1.044 0.29892
## horsepower190 -3.165e+01 1.205e+03 -0.026 0.97911
## horsepower193 1.153e+01 2.872e+01 0.401 0.68904
## horsepower198 -1.458e+01 1.479e+02 -0.099 0.92165
## horsepower200 1.112e+01 1.687e+01 0.659 0.51148
## horsepower208 2.952e+01 3.530e+01 0.836 0.40514
## horsepower210 1.445e+01 1.547e+01 0.934 0.35257
## horsepower215 -9.439e+01 1.161e+02 -0.813 0.41832
## horsepower220 2.897e+01 4.886e+01 0.593 0.55457
## horsepower225 -8.383e+00 1.577e+02 -0.053 0.95772
## horsepower230 2.507e+01 3.372e+01 0.744 0.45895
## horsepower46 1.114e+02 9.519e+01 1.170 0.24476
## horsepower48 -7.562e+00 9.446e+01 -0.080 0.93636
## horsepower49 -4.880e+00 8.794e+00 -0.555 0.58025
## horsepower52 -1.039e+02 1.809e+02 -0.574 0.56730
## horsepower53 -3.206e+02 5.521e+02 -0.581 0.56284
## horsepower54 5.885e+00 1.884e+01 0.312 0.75540
## horsepower58 8.045e+01 1.687e+02 0.477 0.63449
## horsepower60 -2.007e+03 1.287e+03 -1.559 0.12225
## horsepower61 8.094e+00 9.533e+00 0.849 0.39799
## horsepower62 -1.404e+02 1.169e+02 -1.200 0.23300
## horsepower63 -1.671e+01 6.453e+01 -0.259 0.79620
## horsepower64 -1.094e+01 7.677e+00 -1.426 0.15727
## horsepower65 2.662e+01 1.216e+02 0.219 0.82711
## horsepower66 -8.717e+00 1.403e+01 -0.621 0.53577
## horsepower67 1.326e+02 1.174e+02 1.129 0.26166
## horsepower68 8.223e+02 4.136e+02 1.988 0.04967 *
## horsepower69 3.352e+01 3.626e+01 0.924 0.35766
## horsepower70 -9.905e+00 1.077e+02 -0.092 0.92690
## horsepower71 2.212e+01 1.620e+02 0.137 0.89170
## horsepower72 9.706e+01 1.358e+02 0.715 0.47645
## horsepower74 -7.396e+01 1.494e+02 -0.495 0.62181
## horsepower75 -1.986e+01 1.056e+02 -0.188 0.85126
## horsepower76 5.892e+01 7.139e+01 0.825 0.41128
## horsepower77 7.722e+00 2.259e+01 0.342 0.73327
## horsepower78 -2.229e+01 1.160e+02 -0.192 0.84799
## horsepower79 -2.124e+01 4.125e+01 -0.515 0.60783
## horsepower80 9.936e+00 1.085e+02 0.092 0.92725
## horsepower81 4.416e+00 2.682e+01 0.165 0.86958
## horsepower82 -7.312e-01 1.445e+01 -0.051 0.95975
## horsepower83 -9.350e+01 7.996e+01 -1.169 0.24520
## horsepower84 -2.064e+02 2.339e+02 -0.883 0.37961
## horsepower85 5.410e+01 1.094e+02 0.495 0.62201
## horsepower86 -8.048e-01 1.043e+02 -0.008 0.99386
## horsepower87 3.422e+01 1.080e+02 0.317 0.75213
## horsepower88 5.471e+01 9.980e+01 0.548 0.58486
## horsepower89 4.747e+00 4.813e+00 0.986 0.32654
## horsepower90 6.020e+01 1.074e+02 0.560 0.57653
## horsepower91 4.741e-01 7.542e+00 0.063 0.95000
## horsepower92 9.352e+01 1.532e+02 0.610 0.54301
## horsepower93 1.045e+01 7.948e+00 1.315 0.19174
## horsepower94 8.199e+00 8.505e+00 0.964 0.33748
## horsepower95 5.269e+01 1.005e+02 0.525 0.60111
## horsepower96 -1.467e+02 6.580e+01 -2.229 0.02819 *
## horsepower97 3.199e+01 8.251e+01 0.388 0.69913
## horsepower98 -1.424e+01 3.897e+01 -0.366 0.71551
## weight 3.227e-02 4.928e-02 0.655 0.51416
## acceleration -1.285e+01 5.099e+00 -2.520 0.01341 *
## year 1.673e+00 1.795e+00 0.932 0.35361
## origin -5.190e+01 2.205e+01 -2.353 0.02067 *
## cylinders:displacement 2.026e-02 1.812e-02 1.118 0.26622
## cylinders:horsepower100 -4.171e+00 1.336e+01 -0.312 0.75555
## cylinders:horsepower102 NA NA NA NA
## cylinders:horsepower103 NA NA NA NA
## cylinders:horsepower105 -8.858e+00 1.149e+01 -0.771 0.44266
## cylinders:horsepower107 NA NA NA NA
## cylinders:horsepower108 NA NA NA NA
## cylinders:horsepower110 -9.514e+00 1.118e+01 -0.851 0.39705
## cylinders:horsepower112 -3.547e+00 1.031e+01 -0.344 0.73145
## cylinders:horsepower113 NA NA NA NA
## cylinders:horsepower115 2.060e+01 4.341e+01 0.475 0.63618
## cylinders:horsepower116 NA NA NA NA
## cylinders:horsepower120 -9.579e+00 1.242e+01 -0.771 0.44241
## cylinders:horsepower122 NA NA NA NA
## cylinders:horsepower125 -2.950e+00 1.351e+01 -0.218 0.82761
## cylinders:horsepower129 NA NA NA NA
## cylinders:horsepower130 NA NA NA NA
## cylinders:horsepower132 NA NA NA NA
## cylinders:horsepower133 NA NA NA NA
## cylinders:horsepower135 NA NA NA NA
## cylinders:horsepower137 NA NA NA NA
## cylinders:horsepower138 NA NA NA NA
## cylinders:horsepower139 NA NA NA NA
## cylinders:horsepower140 NA NA NA NA
## cylinders:horsepower142 NA NA NA NA
## cylinders:horsepower145 NA NA NA NA
## cylinders:horsepower148 NA NA NA NA
## cylinders:horsepower149 NA NA NA NA
## cylinders:horsepower150 NA NA NA NA
## cylinders:horsepower152 NA NA NA NA
## cylinders:horsepower153 NA NA NA NA
## cylinders:horsepower155 NA NA NA NA
## cylinders:horsepower158 NA NA NA NA
## cylinders:horsepower160 NA NA NA NA
## cylinders:horsepower165 1.949e+01 5.875e+01 0.332 0.74075
## cylinders:horsepower167 NA NA NA NA
## cylinders:horsepower170 NA NA NA NA
## cylinders:horsepower175 NA NA NA NA
## cylinders:horsepower180 NA NA NA NA
## cylinders:horsepower190 NA NA NA NA
## cylinders:horsepower193 NA NA NA NA
## cylinders:horsepower198 NA NA NA NA
## cylinders:horsepower200 NA NA NA NA
## cylinders:horsepower208 NA NA NA NA
## cylinders:horsepower210 NA NA NA NA
## cylinders:horsepower215 NA NA NA NA
## cylinders:horsepower220 NA NA NA NA
## cylinders:horsepower225 NA NA NA NA
## cylinders:horsepower230 NA NA NA NA
## cylinders:horsepower46 NA NA NA NA
## cylinders:horsepower48 NA NA NA NA
## cylinders:horsepower49 NA NA NA NA
## cylinders:horsepower52 NA NA NA NA
## cylinders:horsepower53 NA NA NA NA
## cylinders:horsepower54 NA NA NA NA
## cylinders:horsepower58 NA NA NA NA
## cylinders:horsepower60 NA NA NA NA
## cylinders:horsepower61 NA NA NA NA
## cylinders:horsepower62 NA NA NA NA
## cylinders:horsepower63 NA NA NA NA
## cylinders:horsepower64 NA NA NA NA
## cylinders:horsepower65 NA NA NA NA
## cylinders:horsepower66 NA NA NA NA
## cylinders:horsepower67 -1.626e+01 1.289e+01 -1.262 0.21000
## cylinders:horsepower68 NA NA NA NA
## cylinders:horsepower69 NA NA NA NA
## cylinders:horsepower70 NA NA NA NA
## cylinders:horsepower71 NA NA NA NA
## cylinders:horsepower72 2.313e+01 2.230e+01 1.037 0.30221
## cylinders:horsepower74 NA NA NA NA
## cylinders:horsepower75 NA NA NA NA
## cylinders:horsepower76 -1.288e+01 2.182e+01 -0.590 0.55639
## cylinders:horsepower77 NA NA NA NA
## cylinders:horsepower78 -8.727e+00 1.634e+01 -0.534 0.59462
## cylinders:horsepower79 NA NA NA NA
## cylinders:horsepower80 NA NA NA NA
## cylinders:horsepower81 -3.401e-01 5.163e+00 -0.066 0.94761
## cylinders:horsepower82 NA NA NA NA
## cylinders:horsepower83 NA NA NA NA
## cylinders:horsepower84 NA NA NA NA
## cylinders:horsepower85 -1.528e+01 1.144e+01 -1.336 0.18480
## cylinders:horsepower86 NA NA NA NA
## cylinders:horsepower87 NA NA NA NA
## cylinders:horsepower88 -1.140e+01 1.189e+01 -0.959 0.33993
## cylinders:horsepower89 NA NA NA NA
## cylinders:horsepower90 -1.350e+01 1.192e+01 -1.132 0.26050
## cylinders:horsepower91 NA NA NA NA
## cylinders:horsepower92 NA NA NA NA
## cylinders:horsepower93 NA NA NA NA
## cylinders:horsepower94 NA NA NA NA
## cylinders:horsepower95 -6.456e+00 1.173e+01 -0.550 0.58330
## cylinders:horsepower96 NA NA NA NA
## cylinders:horsepower97 -3.120e+01 1.443e+01 -2.162 0.03314 *
## cylinders:horsepower98 4.593e+00 8.676e+00 0.529 0.59777
## cylinders:weight -3.038e-03 3.487e-03 -0.871 0.38582
## cylinders:acceleration 7.724e-01 5.648e-01 1.368 0.17466
## cylinders:year -2.819e-01 2.906e-01 -0.970 0.33442
## cylinders:origin 6.946e+00 2.993e+00 2.320 0.02246 *
## displacement:horsepower100 1.351e-01 3.503e-01 0.386 0.70067
## displacement:horsepower102 NA NA NA NA
## displacement:horsepower103 NA NA NA NA
## displacement:horsepower105 1.973e-01 3.505e-01 0.563 0.57490
## displacement:horsepower107 NA NA NA NA
## displacement:horsepower108 NA NA NA NA
## displacement:horsepower110 2.162e-01 3.494e-01 0.619 0.53762
## displacement:horsepower112 NA NA NA NA
## displacement:horsepower113 NA NA NA NA
## displacement:horsepower115 -1.363e+00 2.002e+00 -0.681 0.49755
## displacement:horsepower116 NA NA NA NA
## displacement:horsepower120 3.036e-01 3.256e-01 0.933 0.35333
## displacement:horsepower122 NA NA NA NA
## displacement:horsepower125 2.205e-01 3.020e-01 0.730 0.46707
## displacement:horsepower129 NA NA NA NA
## displacement:horsepower130 3.732e-01 7.138e-01 0.523 0.60227
## displacement:horsepower132 NA NA NA NA
## displacement:horsepower133 NA NA NA NA
## displacement:horsepower135 NA NA NA NA
## displacement:horsepower137 NA NA NA NA
## displacement:horsepower138 NA NA NA NA
## displacement:horsepower139 NA NA NA NA
## displacement:horsepower140 -1.100e-01 5.459e-01 -0.201 0.84075
## displacement:horsepower142 NA NA NA NA
## displacement:horsepower145 1.048e-02 3.486e-01 0.030 0.97608
## displacement:horsepower148 NA NA NA NA
## displacement:horsepower149 NA NA NA NA
## displacement:horsepower150 7.687e-02 3.382e-01 0.227 0.82066
## displacement:horsepower152 NA NA NA NA
## displacement:horsepower153 NA NA NA NA
## displacement:horsepower155 NA NA NA NA
## displacement:horsepower158 NA NA NA NA
## displacement:horsepower160 1.423e+00 2.858e+00 0.498 0.61976
## displacement:horsepower165 NA NA NA NA
## displacement:horsepower167 NA NA NA NA
## displacement:horsepower170 2.080e-01 4.844e-01 0.429 0.66856
## displacement:horsepower175 1.585e-01 3.542e-01 0.448 0.65548
## displacement:horsepower180 -1.083e-02 3.622e-01 -0.030 0.97620
## displacement:horsepower190 -7.090e-02 3.640e+00 -0.019 0.98450
## displacement:horsepower193 NA NA NA NA
## displacement:horsepower198 NA NA NA NA
## displacement:horsepower200 NA NA NA NA
## displacement:horsepower208 NA NA NA NA
## displacement:horsepower210 NA NA NA NA
## displacement:horsepower215 1.125e-01 3.918e-01 0.287 0.77456
## displacement:horsepower220 NA NA NA NA
## displacement:horsepower225 NA NA NA NA
## displacement:horsepower230 NA NA NA NA
## displacement:horsepower46 NA NA NA NA
## displacement:horsepower48 NA NA NA NA
## displacement:horsepower49 NA NA NA NA
## displacement:horsepower52 2.356e+00 2.361e+00 0.998 0.32085
## displacement:horsepower53 NA NA NA NA
## displacement:horsepower54 NA NA NA NA
## displacement:horsepower58 NA NA NA NA
## displacement:horsepower60 1.045e+01 6.214e+00 1.682 0.09585 .
## displacement:horsepower61 NA NA NA NA
## displacement:horsepower62 NA NA NA NA
## displacement:horsepower63 2.180e-01 1.200e+00 0.182 0.85624
## displacement:horsepower64 NA NA NA NA
## displacement:horsepower65 -1.244e+00 8.483e-01 -1.466 0.14588
## displacement:horsepower66 NA NA NA NA
## displacement:horsepower67 -1.945e-01 4.796e-01 -0.405 0.68603
## displacement:horsepower68 -4.744e+00 2.472e+00 -1.919 0.05799 .
## displacement:horsepower69 1.415e+00 3.404e+00 0.416 0.67855
## displacement:horsepower70 1.773e-01 4.295e-01 0.413 0.68060
## displacement:horsepower71 4.573e-01 5.558e-01 0.823 0.41269
## displacement:horsepower72 -4.450e-01 4.742e-01 -0.939 0.35036
## displacement:horsepower74 6.818e-01 1.607e+00 0.424 0.67238
## displacement:horsepower75 3.805e-01 3.656e-01 1.041 0.30066
## displacement:horsepower76 5.187e-01 1.325e+00 0.391 0.69637
## displacement:horsepower77 NA NA NA NA
## displacement:horsepower78 1.499e-01 4.144e-01 0.362 0.71829
## displacement:horsepower79 1.381e-01 4.233e-01 0.326 0.74499
## displacement:horsepower80 2.722e-01 4.069e-01 0.669 0.50515
## displacement:horsepower81 NA NA NA NA
## displacement:horsepower82 NA NA NA NA
## displacement:horsepower83 -4.949e-01 5.824e-01 -0.850 0.39760
## displacement:horsepower84 1.485e-01 6.661e-01 0.223 0.82408
## displacement:horsepower85 4.071e-01 3.459e-01 1.177 0.24210
## displacement:horsepower86 -1.616e-01 3.385e-01 -0.478 0.63410
## displacement:horsepower87 -2.162e-01 1.028e+00 -0.210 0.83384
## displacement:horsepower88 2.657e-01 3.551e-01 0.748 0.45608
## displacement:horsepower89 NA NA NA NA
## displacement:horsepower90 3.402e-01 3.637e-01 0.935 0.35200
## displacement:horsepower91 NA NA NA NA
## displacement:horsepower92 -2.984e-01 9.005e-01 -0.331 0.74107
## displacement:horsepower93 NA NA NA NA
## displacement:horsepower94 NA NA NA NA
## displacement:horsepower95 1.900e-01 3.472e-01 0.547 0.58550
## displacement:horsepower96 4.419e-01 5.877e-01 0.752 0.45401
## displacement:horsepower97 5.628e-01 3.590e-01 1.568 0.12024
## displacement:horsepower98 NA NA NA NA
## displacement:weight 2.697e-05 4.853e-05 0.556 0.57971
## displacement:acceleration -1.430e-02 1.296e-02 -1.103 0.27295
## displacement:year 7.138e-03 6.644e-03 1.074 0.28534
## displacement:origin -6.571e-02 6.889e-02 -0.954 0.34261
## horsepower100:weight 1.151e-02 2.152e-02 0.535 0.59408
## horsepower102:weight NA NA NA NA
## horsepower103:weight NA NA NA NA
## horsepower105:weight 8.612e-03 2.179e-02 0.395 0.69361
## horsepower107:weight NA NA NA NA
## horsepower108:weight NA NA NA NA
## horsepower110:weight 6.927e-03 2.182e-02 0.317 0.75164
## horsepower112:weight -6.656e-03 6.231e-02 -0.107 0.91516
## horsepower113:weight NA NA NA NA
## horsepower115:weight 2.438e-01 2.861e-01 0.852 0.39613
## horsepower116:weight NA NA NA NA
## horsepower120:weight 6.289e-03 2.718e-02 0.231 0.81748
## horsepower122:weight NA NA NA NA
## horsepower125:weight NA NA NA NA
## horsepower129:weight 2.365e-02 2.674e-02 0.884 0.37871
## horsepower130:weight 1.841e-02 2.194e-02 0.839 0.40344
## horsepower132:weight NA NA NA NA
## horsepower133:weight NA NA NA NA
## horsepower135:weight NA NA NA NA
## horsepower137:weight NA NA NA NA
## horsepower138:weight NA NA NA NA
## horsepower139:weight 2.514e-02 3.136e-02 0.802 0.42463
## horsepower140:weight 1.372e-02 2.291e-02 0.599 0.55052
## horsepower142:weight NA NA NA NA
## horsepower145:weight 1.719e-02 2.168e-02 0.793 0.42984
## horsepower148:weight NA NA NA NA
## horsepower149:weight NA NA NA NA
## horsepower150:weight 1.693e-02 2.188e-02 0.774 0.44103
## horsepower152:weight NA NA NA NA
## horsepower153:weight 3.689e-02 1.485e-01 0.248 0.80439
## horsepower155:weight 1.034e-02 5.912e-02 0.175 0.86148
## horsepower158:weight NA NA NA NA
## horsepower160:weight NA NA NA NA
## horsepower165:weight -3.330e-03 5.374e-02 -0.062 0.95072
## horsepower167:weight NA NA NA NA
## horsepower170:weight 8.729e-03 3.491e-02 0.250 0.80310
## horsepower175:weight 1.225e-02 2.375e-02 0.516 0.60719
## horsepower180:weight 2.335e-02 2.336e-02 1.000 0.31998
## horsepower190:weight 1.961e-02 6.841e-02 0.287 0.77504
## horsepower193:weight NA NA NA NA
## horsepower198:weight 1.007e-02 2.762e-02 0.365 0.71621
## horsepower200:weight NA NA NA NA
## horsepower208:weight NA NA NA NA
## horsepower210:weight NA NA NA NA
## horsepower215:weight 1.655e-02 3.558e-02 0.465 0.64282
## horsepower220:weight NA NA NA NA
## horsepower225:weight 1.362e-02 2.445e-02 0.557 0.57874
## horsepower230:weight NA NA NA NA
## horsepower46:weight -5.421e-02 5.104e-02 -1.062 0.29091
## horsepower48:weight -3.636e-02 5.442e-02 -0.668 0.50563
## horsepower49:weight NA NA NA NA
## horsepower52:weight 4.577e-02 9.316e-02 0.491 0.62436
## horsepower53:weight NA NA NA NA
## horsepower54:weight NA NA NA NA
## horsepower58:weight -4.481e-02 9.339e-02 -0.480 0.63242
## horsepower60:weight -9.449e-01 5.975e-01 -1.581 0.11711
## horsepower61:weight NA NA NA NA
## horsepower62:weight 7.058e-02 5.977e-02 1.181 0.24061
## horsepower63:weight -5.826e-03 4.241e-02 -0.137 0.89102
## horsepower64:weight NA NA NA NA
## horsepower65:weight 4.180e-02 2.392e-02 1.748 0.08377 .
## horsepower66:weight NA NA NA NA
## horsepower67:weight 5.843e-02 3.061e-02 1.909 0.05927 .
## horsepower68:weight 8.189e-02 5.169e-02 1.584 0.11650
## horsepower69:weight -7.556e-02 1.382e-01 -0.547 0.58575
## horsepower70:weight 1.271e-02 2.525e-02 0.503 0.61602
## horsepower71:weight -3.847e-02 8.397e-02 -0.458 0.64795
## horsepower72:weight 9.655e-03 2.436e-02 0.396 0.69279
## horsepower74:weight 6.035e-04 2.292e-02 0.026 0.97905
## horsepower75:weight -2.578e-04 2.519e-02 -0.010 0.99186
## horsepower76:weight -2.416e-02 9.457e-02 -0.255 0.79892
## horsepower77:weight NA NA NA NA
## horsepower78:weight 1.044e-02 2.263e-02 0.461 0.64560
## horsepower79:weight NA NA NA NA
## horsepower80:weight 2.320e-03 2.227e-02 0.104 0.91725
## horsepower81:weight NA NA NA NA
## horsepower82:weight NA NA NA NA
## horsepower83:weight 5.172e-02 5.269e-02 0.982 0.32873
## horsepower84:weight 2.557e-02 9.183e-02 0.278 0.78126
## horsepower85:weight -8.430e-03 2.090e-02 -0.403 0.68757
## horsepower86:weight 8.641e-03 2.814e-02 0.307 0.75943
## horsepower87:weight NA NA NA NA
## horsepower88:weight -1.692e-03 2.062e-02 -0.082 0.93475
## horsepower89:weight NA NA NA NA
## horsepower90:weight -4.358e-03 2.212e-02 -0.197 0.84427
## horsepower91:weight NA NA NA NA
## horsepower92:weight 2.046e-02 4.034e-02 0.507 0.61320
## horsepower93:weight NA NA NA NA
## horsepower94:weight NA NA NA NA
## horsepower95:weight 6.192e-03 2.126e-02 0.291 0.77150
## horsepower96:weight 3.826e-02 3.282e-02 1.166 0.24662
## horsepower97:weight 2.162e-02 2.612e-02 0.828 0.40984
## horsepower98:weight NA NA NA NA
## horsepower100:acceleration 1.234e-02 2.953e+00 0.004 0.99667
## horsepower102:acceleration NA NA NA NA
## horsepower103:acceleration NA NA NA NA
## horsepower105:acceleration -3.958e-01 2.963e+00 -0.134 0.89401
## horsepower107:acceleration NA NA NA NA
## horsepower108:acceleration NA NA NA NA
## horsepower110:acceleration 1.996e-01 3.064e+00 0.065 0.94818
## horsepower112:acceleration NA NA NA NA
## horsepower113:acceleration NA NA NA NA
## horsepower115:acceleration -1.623e+01 1.783e+01 -0.910 0.36504
## horsepower116:acceleration NA NA NA NA
## horsepower120:acceleration NA NA NA NA
## horsepower122:acceleration NA NA NA NA
## horsepower125:acceleration NA NA NA NA
## horsepower129:acceleration NA NA NA NA
## horsepower130:acceleration -4.823e+00 4.231e+00 -1.140 0.25718
## horsepower132:acceleration NA NA NA NA
## horsepower133:acceleration NA NA NA NA
## horsepower135:acceleration NA NA NA NA
## horsepower137:acceleration NA NA NA NA
## horsepower138:acceleration NA NA NA NA
## horsepower139:acceleration NA NA NA NA
## horsepower140:acceleration -1.132e+00 3.353e+00 -0.338 0.73638
## horsepower142:acceleration NA NA NA NA
## horsepower145:acceleration 1.941e-01 3.541e+00 0.055 0.95641
## horsepower148:acceleration NA NA NA NA
## horsepower149:acceleration NA NA NA NA
## horsepower150:acceleration -9.445e-01 3.159e+00 -0.299 0.76563
## horsepower152:acceleration NA NA NA NA
## horsepower153:acceleration NA NA NA NA
## horsepower155:acceleration NA NA NA NA
## horsepower158:acceleration NA NA NA NA
## horsepower160:acceleration NA NA NA NA
## horsepower165:acceleration 1.684e+01 5.442e+01 0.309 0.75763
## horsepower167:acceleration NA NA NA NA
## horsepower170:acceleration 2.098e+00 1.078e+01 0.195 0.84615
## horsepower175:acceleration 1.134e+00 3.641e+00 0.311 0.75616
## horsepower180:acceleration -2.759e+00 5.587e+00 -0.494 0.62261
## horsepower190:acceleration NA NA NA NA
## horsepower193:acceleration NA NA NA NA
## horsepower198:acceleration NA NA NA NA
## horsepower200:acceleration NA NA NA NA
## horsepower208:acceleration NA NA NA NA
## horsepower210:acceleration NA NA NA NA
## horsepower215:acceleration NA NA NA NA
## horsepower220:acceleration NA NA NA NA
## horsepower225:acceleration -2.020e+00 6.019e+00 -0.336 0.73794
## horsepower230:acceleration NA NA NA NA
## horsepower46:acceleration NA NA NA NA
## horsepower48:acceleration 4.152e+00 6.864e+00 0.605 0.54671
## horsepower49:acceleration NA NA NA NA
## horsepower52:acceleration -8.835e+00 1.000e+01 -0.883 0.37923
## horsepower53:acceleration 1.898e+01 3.167e+01 0.599 0.55050
## horsepower54:acceleration NA NA NA NA
## horsepower58:acceleration NA NA NA NA
## horsepower60:acceleration 5.342e+01 3.557e+01 1.502 0.13644
## horsepower61:acceleration NA NA NA NA
## horsepower62:acceleration NA NA NA NA
## horsepower63:acceleration NA NA NA NA
## horsepower64:acceleration NA NA NA NA
## horsepower65:acceleration -2.099e+00 3.217e+00 -0.653 0.51561
## horsepower66:acceleration NA NA NA NA
## horsepower67:acceleration -4.846e+00 3.454e+00 -1.403 0.16395
## horsepower68:acceleration 2.003e+00 3.367e+00 0.595 0.55330
## horsepower69:acceleration NA NA NA NA
## horsepower70:acceleration 9.337e-01 2.811e+00 0.332 0.74052
## horsepower71:acceleration 3.975e+00 8.327e+00 0.477 0.63423
## horsepower72:acceleration 3.233e-01 2.917e+00 0.111 0.91200
## horsepower74:acceleration NA NA NA NA
## horsepower75:acceleration -6.320e-01 3.162e+00 -0.200 0.84202
## horsepower76:acceleration NA NA NA NA
## horsepower77:acceleration NA NA NA NA
## horsepower78:acceleration -5.101e-01 4.049e+00 -0.126 0.90001
## horsepower79:acceleration NA NA NA NA
## horsepower80:acceleration 1.240e-01 3.069e+00 0.040 0.96786
## horsepower81:acceleration NA NA NA NA
## horsepower82:acceleration NA NA NA NA
## horsepower83:acceleration 1.862e+00 3.596e+00 0.518 0.60582
## horsepower84:acceleration -8.186e-01 5.180e+00 -0.158 0.87477
## horsepower85:acceleration -1.048e+00 2.991e+00 -0.350 0.72681
## horsepower86:acceleration 3.345e-01 2.897e+00 0.115 0.90834
## horsepower87:acceleration NA NA NA NA
## horsepower88:acceleration -1.046e+00 2.956e+00 -0.354 0.72423
## horsepower89:acceleration NA NA NA NA
## horsepower90:acceleration 4.018e-01 2.786e+00 0.144 0.88565
## horsepower91:acceleration NA NA NA NA
## horsepower92:acceleration -5.828e+00 5.576e+00 -1.045 0.29860
## horsepower93:acceleration NA NA NA NA
## horsepower94:acceleration NA NA NA NA
## horsepower95:acceleration 5.476e-01 2.904e+00 0.189 0.85081
## horsepower96:acceleration NA NA NA NA
## horsepower97:acceleration -1.075e+00 3.782e+00 -0.284 0.77689
## horsepower98:acceleration NA NA NA NA
## horsepower100:year -6.954e-01 8.333e-01 -0.834 0.40613
## horsepower102:year NA NA NA NA
## horsepower103:year NA NA NA NA
## horsepower105:year -2.564e-01 7.527e-01 -0.341 0.73418
## horsepower107:year NA NA NA NA
## horsepower108:year NA NA NA NA
## horsepower110:year -3.447e-01 7.394e-01 -0.466 0.64215
## horsepower112:year NA NA NA NA
## horsepower113:year NA NA NA NA
## horsepower115:year NA NA NA NA
## horsepower116:year NA NA NA NA
## horsepower120:year NA NA NA NA
## horsepower122:year NA NA NA NA
## horsepower125:year NA NA NA NA
## horsepower129:year NA NA NA NA
## horsepower130:year 1.108e+00 1.244e+00 0.891 0.37505
## horsepower132:year NA NA NA NA
## horsepower133:year NA NA NA NA
## horsepower135:year NA NA NA NA
## horsepower137:year NA NA NA NA
## horsepower138:year NA NA NA NA
## horsepower139:year NA NA NA NA
## horsepower140:year 8.780e-01 1.254e+00 0.700 0.48566
## horsepower142:year NA NA NA NA
## horsepower145:year -6.692e-01 1.213e+00 -0.552 0.58256
## horsepower148:year NA NA NA NA
## horsepower149:year NA NA NA NA
## horsepower150:year -7.841e-02 8.186e-01 -0.096 0.92389
## horsepower152:year NA NA NA NA
## horsepower153:year NA NA NA NA
## horsepower155:year NA NA NA NA
## horsepower158:year NA NA NA NA
## horsepower160:year NA NA NA NA
## horsepower165:year NA NA NA NA
## horsepower167:year NA NA NA NA
## horsepower170:year 5.960e-01 1.906e+00 0.313 0.75521
## horsepower175:year -8.628e-01 3.595e+00 -0.240 0.81087
## horsepower180:year 1.276e+00 1.188e+00 1.074 0.28542
## horsepower190:year NA NA NA NA
## horsepower193:year NA NA NA NA
## horsepower198:year NA NA NA NA
## horsepower200:year NA NA NA NA
## horsepower208:year NA NA NA NA
## horsepower210:year NA NA NA NA
## horsepower215:year NA NA NA NA
## horsepower220:year NA NA NA NA
## horsepower225:year NA NA NA NA
## horsepower230:year NA NA NA NA
## horsepower46:year NA NA NA NA
## horsepower48:year NA NA NA NA
## horsepower49:year NA NA NA NA
## horsepower52:year NA NA NA NA
## horsepower53:year NA NA NA NA
## horsepower54:year NA NA NA NA
## horsepower58:year NA NA NA NA
## horsepower60:year 2.423e+01 1.561e+01 1.552 0.12396
## horsepower61:year NA NA NA NA
## horsepower62:year NA NA NA NA
## horsepower63:year NA NA NA NA
## horsepower64:year NA NA NA NA
## horsepower65:year 3.560e-01 1.215e+00 0.293 0.77011
## horsepower66:year NA NA NA NA
## horsepower67:year -2.038e+00 8.229e-01 -2.477 0.01503 *
## horsepower68:year -7.474e+00 3.231e+00 -2.313 0.02289 *
## horsepower69:year NA NA NA NA
## horsepower70:year -8.037e-01 7.300e-01 -1.101 0.27365
## horsepower71:year -6.422e-01 1.602e+00 -0.401 0.68935
## horsepower72:year -2.023e+00 1.498e+00 -1.351 0.18002
## horsepower74:year NA NA NA NA
## horsepower75:year -3.062e-01 6.715e-01 -0.456 0.64947
## horsepower76:year NA NA NA NA
## horsepower77:year NA NA NA NA
## horsepower78:year 3.401e-01 1.046e+00 0.325 0.74581
## horsepower79:year NA NA NA NA
## horsepower80:year -7.409e-01 8.311e-01 -0.891 0.37492
## horsepower81:year NA NA NA NA
## horsepower82:year NA NA NA NA
## horsepower83:year NA NA NA NA
## horsepower84:year 1.631e+00 2.197e+00 0.742 0.45967
## horsepower85:year -6.066e-02 6.780e-01 -0.089 0.92890
## horsepower86:year -7.022e-02 1.092e+00 -0.064 0.94885
## horsepower87:year NA NA NA NA
## horsepower88:year -3.455e-01 5.134e-01 -0.673 0.50255
## horsepower89:year NA NA NA NA
## horsepower90:year -6.671e-01 6.674e-01 -0.999 0.32012
## horsepower91:year NA NA NA NA
## horsepower92:year -2.782e-01 2.233e+00 -0.125 0.90112
## horsepower93:year NA NA NA NA
## horsepower94:year NA NA NA NA
## horsepower95:year -1.187e+00 6.098e-01 -1.946 0.05462 .
## horsepower96:year NA NA NA NA
## horsepower97:year NA NA NA NA
## horsepower98:year NA NA NA NA
## horsepower100:origin 1.126e+01 6.084e+00 1.850 0.06737 .
## horsepower102:origin NA NA NA NA
## horsepower103:origin NA NA NA NA
## horsepower105:origin NA NA NA NA
## horsepower107:origin NA NA NA NA
## horsepower108:origin NA NA NA NA
## horsepower110:origin 6.518e+00 7.258e+00 0.898 0.37148
## horsepower112:origin NA NA NA NA
## horsepower113:origin NA NA NA NA
## horsepower115:origin NA NA NA NA
## horsepower116:origin NA NA NA NA
## horsepower120:origin NA NA NA NA
## horsepower122:origin NA NA NA NA
## horsepower125:origin NA NA NA NA
## horsepower129:origin NA NA NA NA
## horsepower130:origin NA NA NA NA
## horsepower132:origin NA NA NA NA
## horsepower133:origin NA NA NA NA
## horsepower135:origin NA NA NA NA
## horsepower137:origin NA NA NA NA
## horsepower138:origin NA NA NA NA
## horsepower139:origin NA NA NA NA
## horsepower140:origin NA NA NA NA
## horsepower142:origin NA NA NA NA
## horsepower145:origin NA NA NA NA
## horsepower148:origin NA NA NA NA
## horsepower149:origin NA NA NA NA
## horsepower150:origin NA NA NA NA
## horsepower152:origin NA NA NA NA
## horsepower153:origin NA NA NA NA
## horsepower155:origin NA NA NA NA
## horsepower158:origin NA NA NA NA
## horsepower160:origin NA NA NA NA
## horsepower165:origin NA NA NA NA
## horsepower167:origin NA NA NA NA
## horsepower170:origin NA NA NA NA
## horsepower175:origin NA NA NA NA
## horsepower180:origin NA NA NA NA
## horsepower190:origin NA NA NA NA
## horsepower193:origin NA NA NA NA
## horsepower198:origin NA NA NA NA
## horsepower200:origin NA NA NA NA
## horsepower208:origin NA NA NA NA
## horsepower210:origin NA NA NA NA
## horsepower215:origin NA NA NA NA
## horsepower220:origin NA NA NA NA
## horsepower225:origin NA NA NA NA
## horsepower230:origin NA NA NA NA
## horsepower46:origin NA NA NA NA
## horsepower48:origin NA NA NA NA
## horsepower49:origin NA NA NA NA
## horsepower52:origin NA NA NA NA
## horsepower53:origin NA NA NA NA
## horsepower54:origin NA NA NA NA
## horsepower58:origin NA NA NA NA
## horsepower60:origin NA NA NA NA
## horsepower61:origin NA NA NA NA
## horsepower62:origin NA NA NA NA
## horsepower63:origin NA NA NA NA
## horsepower64:origin NA NA NA NA
## horsepower65:origin 2.848e+00 6.803e+00 0.419 0.67641
## horsepower66:origin NA NA NA NA
## horsepower67:origin 2.719e+01 7.465e+00 3.642 0.00044 ***
## horsepower68:origin 7.419e+00 5.084e+00 1.459 0.14785
## horsepower69:origin NA NA NA NA
## horsepower70:origin 6.839e+00 5.278e+00 1.296 0.19819
## horsepower71:origin NA NA NA NA
## horsepower72:origin NA NA NA NA
## horsepower74:origin NA NA NA NA
## horsepower75:origin 7.355e+00 4.596e+00 1.600 0.11284
## horsepower76:origin NA NA NA NA
## horsepower77:origin NA NA NA NA
## horsepower78:origin NA NA NA NA
## horsepower79:origin NA NA NA NA
## horsepower80:origin 5.871e+00 1.160e+01 0.506 0.61406
## horsepower81:origin NA NA NA NA
## horsepower82:origin NA NA NA NA
## horsepower83:origin NA NA NA NA
## horsepower84:origin NA NA NA NA
## horsepower85:origin NA NA NA NA
## horsepower86:origin NA NA NA NA
## horsepower87:origin NA NA NA NA
## horsepower88:origin 6.744e+00 5.202e+00 1.296 0.19798
## horsepower89:origin NA NA NA NA
## horsepower90:origin 7.298e+00 5.105e+00 1.430 0.15608
## horsepower91:origin NA NA NA NA
## horsepower92:origin 6.428e+00 1.560e+01 0.412 0.68116
## horsepower93:origin NA NA NA NA
## horsepower94:origin NA NA NA NA
## horsepower95:origin 9.668e+00 5.287e+00 1.829 0.07060 .
## horsepower96:origin NA NA NA NA
## horsepower97:origin NA NA NA NA
## horsepower98:origin NA NA NA NA
## weight:acceleration 8.711e-04 5.749e-04 1.515 0.13303
## weight:year -6.974e-04 4.908e-04 -1.421 0.15862
## weight:origin 6.247e-03 4.270e-03 1.463 0.14678
## acceleration:year 1.038e-01 6.789e-02 1.529 0.12970
## acceleration:origin 4.422e-01 4.026e-01 1.098 0.27489
## year:origin 3.657e-02 2.517e-01 0.145 0.88477
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.201 on 95 degrees of freedom
## Multiple R-squared: 0.981, Adjusted R-squared: 0.9209
## F-statistic: 16.31 on 301 and 95 DF, p-value: < 2.2e-16y3<-lm(mpg~.*.,Auto1)
summary(y3)##
## Call:
## lm(formula = mpg ~ . * ., data = Auto1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5941 -0.1449 0.0000 0.0616 6.0550
##
## Coefficients: (371 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.438e+01 1.542e+02 0.158 0.87466
## cylinders 1.723e+01 2.322e+01 0.742 0.45978
## displacement -6.631e-01 5.624e-01 -1.179 0.24131
## horsepower100 5.188e+00 1.103e+02 0.047 0.96257
## horsepower102 4.878e+00 1.069e+01 0.456 0.64926
## horsepower103 -1.338e+01 1.118e+01 -1.197 0.23417
## horsepower105 1.336e+01 1.087e+02 0.123 0.90239
## horsepower107 -1.558e+01 1.527e+01 -1.021 0.31005
## horsepower108 -2.806e+01 1.509e+01 -1.860 0.06595 .
## horsepower110 8.079e+00 1.097e+02 0.074 0.94144
## horsepower112 3.662e+01 1.897e+02 0.193 0.84730
## horsepower113 9.789e+00 1.734e+01 0.565 0.57372
## horsepower115 -3.441e+02 4.583e+02 -0.751 0.45465
## horsepower116 -1.729e+01 1.423e+01 -1.215 0.22735
## horsepower120 -3.166e+01 5.687e+01 -0.557 0.57898
## horsepower122 -2.300e+01 1.525e+01 -1.508 0.13480
## horsepower125 -3.619e+01 2.639e+01 -1.371 0.17347
## horsepower129 -8.259e+01 1.040e+02 -0.794 0.42923
## horsepower130 -1.922e+02 2.513e+02 -0.765 0.44629
## horsepower132 -7.480e+00 1.694e+01 -0.441 0.65986
## horsepower133 -1.870e+01 2.120e+01 -0.882 0.38011
## horsepower135 8.390e+00 1.175e+01 0.714 0.47680
## horsepower137 9.056e+00 1.239e+01 0.731 0.46643
## horsepower138 1.361e+01 1.979e+01 0.688 0.49319
## horsepower139 -8.403e+01 1.220e+02 -0.689 0.49280
## horsepower140 -5.996e+01 1.404e+02 -0.427 0.67035
## horsepower142 1.405e+01 1.755e+01 0.801 0.42524
## horsepower145 -1.095e+01 1.547e+02 -0.071 0.94371
## horsepower148 2.524e+01 1.681e+01 1.502 0.13640
## horsepower149 2.062e+01 1.573e+01 1.311 0.19306
## horsepower150 -6.253e+01 1.172e+02 -0.533 0.59495
## horsepower152 1.809e+01 1.743e+01 1.038 0.30199
## horsepower153 -1.346e+02 6.190e+02 -0.217 0.82831
## horsepower155 -2.439e+01 2.628e+02 -0.093 0.92625
## horsepower158 1.999e+01 1.624e+01 1.231 0.22147
## horsepower160 -4.774e+02 1.001e+03 -0.477 0.63433
## horsepower165 -3.251e+02 9.086e+02 -0.358 0.72130
## horsepower167 3.244e+01 2.478e+01 1.309 0.19378
## horsepower170 -1.607e+02 2.833e+02 -0.567 0.57183
## horsepower175 -4.179e+01 3.129e+02 -0.134 0.89401
## horsepower180 -1.388e+02 1.329e+02 -1.044 0.29892
## horsepower190 -3.165e+01 1.205e+03 -0.026 0.97911
## horsepower193 1.153e+01 2.872e+01 0.401 0.68904
## horsepower198 -1.458e+01 1.479e+02 -0.099 0.92165
## horsepower200 1.112e+01 1.687e+01 0.659 0.51148
## horsepower208 2.952e+01 3.530e+01 0.836 0.40514
## horsepower210 1.445e+01 1.547e+01 0.934 0.35257
## horsepower215 -9.439e+01 1.161e+02 -0.813 0.41832
## horsepower220 2.897e+01 4.886e+01 0.593 0.55457
## horsepower225 -8.383e+00 1.577e+02 -0.053 0.95772
## horsepower230 2.507e+01 3.372e+01 0.744 0.45895
## horsepower46 1.114e+02 9.519e+01 1.170 0.24476
## horsepower48 -7.562e+00 9.446e+01 -0.080 0.93636
## horsepower49 -4.880e+00 8.794e+00 -0.555 0.58025
## horsepower52 -1.039e+02 1.809e+02 -0.574 0.56730
## horsepower53 -3.206e+02 5.521e+02 -0.581 0.56284
## horsepower54 5.885e+00 1.884e+01 0.312 0.75540
## horsepower58 8.045e+01 1.687e+02 0.477 0.63449
## horsepower60 -2.007e+03 1.287e+03 -1.559 0.12225
## horsepower61 8.094e+00 9.533e+00 0.849 0.39799
## horsepower62 -1.404e+02 1.169e+02 -1.200 0.23300
## horsepower63 -1.671e+01 6.453e+01 -0.259 0.79620
## horsepower64 -1.094e+01 7.677e+00 -1.426 0.15727
## horsepower65 2.662e+01 1.216e+02 0.219 0.82711
## horsepower66 -8.717e+00 1.403e+01 -0.621 0.53577
## horsepower67 1.326e+02 1.174e+02 1.129 0.26166
## horsepower68 8.223e+02 4.136e+02 1.988 0.04967 *
## horsepower69 3.352e+01 3.626e+01 0.924 0.35766
## horsepower70 -9.905e+00 1.077e+02 -0.092 0.92690
## horsepower71 2.212e+01 1.620e+02 0.137 0.89170
## horsepower72 9.706e+01 1.358e+02 0.715 0.47645
## horsepower74 -7.396e+01 1.494e+02 -0.495 0.62181
## horsepower75 -1.986e+01 1.056e+02 -0.188 0.85126
## horsepower76 5.892e+01 7.139e+01 0.825 0.41128
## horsepower77 7.722e+00 2.259e+01 0.342 0.73327
## horsepower78 -2.229e+01 1.160e+02 -0.192 0.84799
## horsepower79 -2.124e+01 4.125e+01 -0.515 0.60783
## horsepower80 9.936e+00 1.085e+02 0.092 0.92725
## horsepower81 4.416e+00 2.682e+01 0.165 0.86958
## horsepower82 -7.312e-01 1.445e+01 -0.051 0.95975
## horsepower83 -9.350e+01 7.996e+01 -1.169 0.24520
## horsepower84 -2.064e+02 2.339e+02 -0.883 0.37961
## horsepower85 5.410e+01 1.094e+02 0.495 0.62201
## horsepower86 -8.048e-01 1.043e+02 -0.008 0.99386
## horsepower87 3.422e+01 1.080e+02 0.317 0.75213
## horsepower88 5.471e+01 9.980e+01 0.548 0.58486
## horsepower89 4.747e+00 4.813e+00 0.986 0.32654
## horsepower90 6.020e+01 1.074e+02 0.560 0.57653
## horsepower91 4.741e-01 7.542e+00 0.063 0.95000
## horsepower92 9.352e+01 1.532e+02 0.610 0.54301
## horsepower93 1.045e+01 7.948e+00 1.315 0.19174
## horsepower94 8.199e+00 8.505e+00 0.964 0.33748
## horsepower95 5.269e+01 1.005e+02 0.525 0.60111
## horsepower96 -1.467e+02 6.580e+01 -2.229 0.02819 *
## horsepower97 3.199e+01 8.251e+01 0.388 0.69913
## horsepower98 -1.424e+01 3.897e+01 -0.366 0.71551
## weight 3.227e-02 4.928e-02 0.655 0.51416
## acceleration -1.285e+01 5.099e+00 -2.520 0.01341 *
## year 1.673e+00 1.795e+00 0.932 0.35361
## origin -5.190e+01 2.205e+01 -2.353 0.02067 *
## cylinders:displacement 2.026e-02 1.812e-02 1.118 0.26622
## cylinders:horsepower100 -4.171e+00 1.336e+01 -0.312 0.75555
## cylinders:horsepower102 NA NA NA NA
## cylinders:horsepower103 NA NA NA NA
## cylinders:horsepower105 -8.858e+00 1.149e+01 -0.771 0.44266
## cylinders:horsepower107 NA NA NA NA
## cylinders:horsepower108 NA NA NA NA
## cylinders:horsepower110 -9.514e+00 1.118e+01 -0.851 0.39705
## cylinders:horsepower112 -3.547e+00 1.031e+01 -0.344 0.73145
## cylinders:horsepower113 NA NA NA NA
## cylinders:horsepower115 2.060e+01 4.341e+01 0.475 0.63618
## cylinders:horsepower116 NA NA NA NA
## cylinders:horsepower120 -9.579e+00 1.242e+01 -0.771 0.44241
## cylinders:horsepower122 NA NA NA NA
## cylinders:horsepower125 -2.950e+00 1.351e+01 -0.218 0.82761
## cylinders:horsepower129 NA NA NA NA
## cylinders:horsepower130 NA NA NA NA
## cylinders:horsepower132 NA NA NA NA
## cylinders:horsepower133 NA NA NA NA
## cylinders:horsepower135 NA NA NA NA
## cylinders:horsepower137 NA NA NA NA
## cylinders:horsepower138 NA NA NA NA
## cylinders:horsepower139 NA NA NA NA
## cylinders:horsepower140 NA NA NA NA
## cylinders:horsepower142 NA NA NA NA
## cylinders:horsepower145 NA NA NA NA
## cylinders:horsepower148 NA NA NA NA
## cylinders:horsepower149 NA NA NA NA
## cylinders:horsepower150 NA NA NA NA
## cylinders:horsepower152 NA NA NA NA
## cylinders:horsepower153 NA NA NA NA
## cylinders:horsepower155 NA NA NA NA
## cylinders:horsepower158 NA NA NA NA
## cylinders:horsepower160 NA NA NA NA
## cylinders:horsepower165 1.949e+01 5.875e+01 0.332 0.74075
## cylinders:horsepower167 NA NA NA NA
## cylinders:horsepower170 NA NA NA NA
## cylinders:horsepower175 NA NA NA NA
## cylinders:horsepower180 NA NA NA NA
## cylinders:horsepower190 NA NA NA NA
## cylinders:horsepower193 NA NA NA NA
## cylinders:horsepower198 NA NA NA NA
## cylinders:horsepower200 NA NA NA NA
## cylinders:horsepower208 NA NA NA NA
## cylinders:horsepower210 NA NA NA NA
## cylinders:horsepower215 NA NA NA NA
## cylinders:horsepower220 NA NA NA NA
## cylinders:horsepower225 NA NA NA NA
## cylinders:horsepower230 NA NA NA NA
## cylinders:horsepower46 NA NA NA NA
## cylinders:horsepower48 NA NA NA NA
## cylinders:horsepower49 NA NA NA NA
## cylinders:horsepower52 NA NA NA NA
## cylinders:horsepower53 NA NA NA NA
## cylinders:horsepower54 NA NA NA NA
## cylinders:horsepower58 NA NA NA NA
## cylinders:horsepower60 NA NA NA NA
## cylinders:horsepower61 NA NA NA NA
## cylinders:horsepower62 NA NA NA NA
## cylinders:horsepower63 NA NA NA NA
## cylinders:horsepower64 NA NA NA NA
## cylinders:horsepower65 NA NA NA NA
## cylinders:horsepower66 NA NA NA NA
## cylinders:horsepower67 -1.626e+01 1.289e+01 -1.262 0.21000
## cylinders:horsepower68 NA NA NA NA
## cylinders:horsepower69 NA NA NA NA
## cylinders:horsepower70 NA NA NA NA
## cylinders:horsepower71 NA NA NA NA
## cylinders:horsepower72 2.313e+01 2.230e+01 1.037 0.30221
## cylinders:horsepower74 NA NA NA NA
## cylinders:horsepower75 NA NA NA NA
## cylinders:horsepower76 -1.288e+01 2.182e+01 -0.590 0.55639
## cylinders:horsepower77 NA NA NA NA
## cylinders:horsepower78 -8.727e+00 1.634e+01 -0.534 0.59462
## cylinders:horsepower79 NA NA NA NA
## cylinders:horsepower80 NA NA NA NA
## cylinders:horsepower81 -3.401e-01 5.163e+00 -0.066 0.94761
## cylinders:horsepower82 NA NA NA NA
## cylinders:horsepower83 NA NA NA NA
## cylinders:horsepower84 NA NA NA NA
## cylinders:horsepower85 -1.528e+01 1.144e+01 -1.336 0.18480
## cylinders:horsepower86 NA NA NA NA
## cylinders:horsepower87 NA NA NA NA
## cylinders:horsepower88 -1.140e+01 1.189e+01 -0.959 0.33993
## cylinders:horsepower89 NA NA NA NA
## cylinders:horsepower90 -1.350e+01 1.192e+01 -1.132 0.26050
## cylinders:horsepower91 NA NA NA NA
## cylinders:horsepower92 NA NA NA NA
## cylinders:horsepower93 NA NA NA NA
## cylinders:horsepower94 NA NA NA NA
## cylinders:horsepower95 -6.456e+00 1.173e+01 -0.550 0.58330
## cylinders:horsepower96 NA NA NA NA
## cylinders:horsepower97 -3.120e+01 1.443e+01 -2.162 0.03314 *
## cylinders:horsepower98 4.593e+00 8.676e+00 0.529 0.59777
## cylinders:weight -3.038e-03 3.487e-03 -0.871 0.38582
## cylinders:acceleration 7.724e-01 5.648e-01 1.368 0.17466
## cylinders:year -2.819e-01 2.906e-01 -0.970 0.33442
## cylinders:origin 6.946e+00 2.993e+00 2.320 0.02246 *
## displacement:horsepower100 1.351e-01 3.503e-01 0.386 0.70067
## displacement:horsepower102 NA NA NA NA
## displacement:horsepower103 NA NA NA NA
## displacement:horsepower105 1.973e-01 3.505e-01 0.563 0.57490
## displacement:horsepower107 NA NA NA NA
## displacement:horsepower108 NA NA NA NA
## displacement:horsepower110 2.162e-01 3.494e-01 0.619 0.53762
## displacement:horsepower112 NA NA NA NA
## displacement:horsepower113 NA NA NA NA
## displacement:horsepower115 -1.363e+00 2.002e+00 -0.681 0.49755
## displacement:horsepower116 NA NA NA NA
## displacement:horsepower120 3.036e-01 3.256e-01 0.933 0.35333
## displacement:horsepower122 NA NA NA NA
## displacement:horsepower125 2.205e-01 3.020e-01 0.730 0.46707
## displacement:horsepower129 NA NA NA NA
## displacement:horsepower130 3.732e-01 7.138e-01 0.523 0.60227
## displacement:horsepower132 NA NA NA NA
## displacement:horsepower133 NA NA NA NA
## displacement:horsepower135 NA NA NA NA
## displacement:horsepower137 NA NA NA NA
## displacement:horsepower138 NA NA NA NA
## displacement:horsepower139 NA NA NA NA
## displacement:horsepower140 -1.100e-01 5.459e-01 -0.201 0.84075
## displacement:horsepower142 NA NA NA NA
## displacement:horsepower145 1.048e-02 3.486e-01 0.030 0.97608
## displacement:horsepower148 NA NA NA NA
## displacement:horsepower149 NA NA NA NA
## displacement:horsepower150 7.687e-02 3.382e-01 0.227 0.82066
## displacement:horsepower152 NA NA NA NA
## displacement:horsepower153 NA NA NA NA
## displacement:horsepower155 NA NA NA NA
## displacement:horsepower158 NA NA NA NA
## displacement:horsepower160 1.423e+00 2.858e+00 0.498 0.61976
## displacement:horsepower165 NA NA NA NA
## displacement:horsepower167 NA NA NA NA
## displacement:horsepower170 2.080e-01 4.844e-01 0.429 0.66856
## displacement:horsepower175 1.585e-01 3.542e-01 0.448 0.65548
## displacement:horsepower180 -1.083e-02 3.622e-01 -0.030 0.97620
## displacement:horsepower190 -7.090e-02 3.640e+00 -0.019 0.98450
## displacement:horsepower193 NA NA NA NA
## displacement:horsepower198 NA NA NA NA
## displacement:horsepower200 NA NA NA NA
## displacement:horsepower208 NA NA NA NA
## displacement:horsepower210 NA NA NA NA
## displacement:horsepower215 1.125e-01 3.918e-01 0.287 0.77456
## displacement:horsepower220 NA NA NA NA
## displacement:horsepower225 NA NA NA NA
## displacement:horsepower230 NA NA NA NA
## displacement:horsepower46 NA NA NA NA
## displacement:horsepower48 NA NA NA NA
## displacement:horsepower49 NA NA NA NA
## displacement:horsepower52 2.356e+00 2.361e+00 0.998 0.32085
## displacement:horsepower53 NA NA NA NA
## displacement:horsepower54 NA NA NA NA
## displacement:horsepower58 NA NA NA NA
## displacement:horsepower60 1.045e+01 6.214e+00 1.682 0.09585 .
## displacement:horsepower61 NA NA NA NA
## displacement:horsepower62 NA NA NA NA
## displacement:horsepower63 2.180e-01 1.200e+00 0.182 0.85624
## displacement:horsepower64 NA NA NA NA
## displacement:horsepower65 -1.244e+00 8.483e-01 -1.466 0.14588
## displacement:horsepower66 NA NA NA NA
## displacement:horsepower67 -1.945e-01 4.796e-01 -0.405 0.68603
## displacement:horsepower68 -4.744e+00 2.472e+00 -1.919 0.05799 .
## displacement:horsepower69 1.415e+00 3.404e+00 0.416 0.67855
## displacement:horsepower70 1.773e-01 4.295e-01 0.413 0.68060
## displacement:horsepower71 4.573e-01 5.558e-01 0.823 0.41269
## displacement:horsepower72 -4.450e-01 4.742e-01 -0.939 0.35036
## displacement:horsepower74 6.818e-01 1.607e+00 0.424 0.67238
## displacement:horsepower75 3.805e-01 3.656e-01 1.041 0.30066
## displacement:horsepower76 5.187e-01 1.325e+00 0.391 0.69637
## displacement:horsepower77 NA NA NA NA
## displacement:horsepower78 1.499e-01 4.144e-01 0.362 0.71829
## displacement:horsepower79 1.381e-01 4.233e-01 0.326 0.74499
## displacement:horsepower80 2.722e-01 4.069e-01 0.669 0.50515
## displacement:horsepower81 NA NA NA NA
## displacement:horsepower82 NA NA NA NA
## displacement:horsepower83 -4.949e-01 5.824e-01 -0.850 0.39760
## displacement:horsepower84 1.485e-01 6.661e-01 0.223 0.82408
## displacement:horsepower85 4.071e-01 3.459e-01 1.177 0.24210
## displacement:horsepower86 -1.616e-01 3.385e-01 -0.478 0.63410
## displacement:horsepower87 -2.162e-01 1.028e+00 -0.210 0.83384
## displacement:horsepower88 2.657e-01 3.551e-01 0.748 0.45608
## displacement:horsepower89 NA NA NA NA
## displacement:horsepower90 3.402e-01 3.637e-01 0.935 0.35200
## displacement:horsepower91 NA NA NA NA
## displacement:horsepower92 -2.984e-01 9.005e-01 -0.331 0.74107
## displacement:horsepower93 NA NA NA NA
## displacement:horsepower94 NA NA NA NA
## displacement:horsepower95 1.900e-01 3.472e-01 0.547 0.58550
## displacement:horsepower96 4.419e-01 5.877e-01 0.752 0.45401
## displacement:horsepower97 5.628e-01 3.590e-01 1.568 0.12024
## displacement:horsepower98 NA NA NA NA
## displacement:weight 2.697e-05 4.853e-05 0.556 0.57971
## displacement:acceleration -1.430e-02 1.296e-02 -1.103 0.27295
## displacement:year 7.138e-03 6.644e-03 1.074 0.28534
## displacement:origin -6.571e-02 6.889e-02 -0.954 0.34261
## horsepower100:weight 1.151e-02 2.152e-02 0.535 0.59408
## horsepower102:weight NA NA NA NA
## horsepower103:weight NA NA NA NA
## horsepower105:weight 8.612e-03 2.179e-02 0.395 0.69361
## horsepower107:weight NA NA NA NA
## horsepower108:weight NA NA NA NA
## horsepower110:weight 6.927e-03 2.182e-02 0.317 0.75164
## horsepower112:weight -6.656e-03 6.231e-02 -0.107 0.91516
## horsepower113:weight NA NA NA NA
## horsepower115:weight 2.438e-01 2.861e-01 0.852 0.39613
## horsepower116:weight NA NA NA NA
## horsepower120:weight 6.289e-03 2.718e-02 0.231 0.81748
## horsepower122:weight NA NA NA NA
## horsepower125:weight NA NA NA NA
## horsepower129:weight 2.365e-02 2.674e-02 0.884 0.37871
## horsepower130:weight 1.841e-02 2.194e-02 0.839 0.40344
## horsepower132:weight NA NA NA NA
## horsepower133:weight NA NA NA NA
## horsepower135:weight NA NA NA NA
## horsepower137:weight NA NA NA NA
## horsepower138:weight NA NA NA NA
## horsepower139:weight 2.514e-02 3.136e-02 0.802 0.42463
## horsepower140:weight 1.372e-02 2.291e-02 0.599 0.55052
## horsepower142:weight NA NA NA NA
## horsepower145:weight 1.719e-02 2.168e-02 0.793 0.42984
## horsepower148:weight NA NA NA NA
## horsepower149:weight NA NA NA NA
## horsepower150:weight 1.693e-02 2.188e-02 0.774 0.44103
## horsepower152:weight NA NA NA NA
## horsepower153:weight 3.689e-02 1.485e-01 0.248 0.80439
## horsepower155:weight 1.034e-02 5.912e-02 0.175 0.86148
## horsepower158:weight NA NA NA NA
## horsepower160:weight NA NA NA NA
## horsepower165:weight -3.330e-03 5.374e-02 -0.062 0.95072
## horsepower167:weight NA NA NA NA
## horsepower170:weight 8.729e-03 3.491e-02 0.250 0.80310
## horsepower175:weight 1.225e-02 2.375e-02 0.516 0.60719
## horsepower180:weight 2.335e-02 2.336e-02 1.000 0.31998
## horsepower190:weight 1.961e-02 6.841e-02 0.287 0.77504
## horsepower193:weight NA NA NA NA
## horsepower198:weight 1.007e-02 2.762e-02 0.365 0.71621
## horsepower200:weight NA NA NA NA
## horsepower208:weight NA NA NA NA
## horsepower210:weight NA NA NA NA
## horsepower215:weight 1.655e-02 3.558e-02 0.465 0.64282
## horsepower220:weight NA NA NA NA
## horsepower225:weight 1.362e-02 2.445e-02 0.557 0.57874
## horsepower230:weight NA NA NA NA
## horsepower46:weight -5.421e-02 5.104e-02 -1.062 0.29091
## horsepower48:weight -3.636e-02 5.442e-02 -0.668 0.50563
## horsepower49:weight NA NA NA NA
## horsepower52:weight 4.577e-02 9.316e-02 0.491 0.62436
## horsepower53:weight NA NA NA NA
## horsepower54:weight NA NA NA NA
## horsepower58:weight -4.481e-02 9.339e-02 -0.480 0.63242
## horsepower60:weight -9.449e-01 5.975e-01 -1.581 0.11711
## horsepower61:weight NA NA NA NA
## horsepower62:weight 7.058e-02 5.977e-02 1.181 0.24061
## horsepower63:weight -5.826e-03 4.241e-02 -0.137 0.89102
## horsepower64:weight NA NA NA NA
## horsepower65:weight 4.180e-02 2.392e-02 1.748 0.08377 .
## horsepower66:weight NA NA NA NA
## horsepower67:weight 5.843e-02 3.061e-02 1.909 0.05927 .
## horsepower68:weight 8.189e-02 5.169e-02 1.584 0.11650
## horsepower69:weight -7.556e-02 1.382e-01 -0.547 0.58575
## horsepower70:weight 1.271e-02 2.525e-02 0.503 0.61602
## horsepower71:weight -3.847e-02 8.397e-02 -0.458 0.64795
## horsepower72:weight 9.655e-03 2.436e-02 0.396 0.69279
## horsepower74:weight 6.035e-04 2.292e-02 0.026 0.97905
## horsepower75:weight -2.578e-04 2.519e-02 -0.010 0.99186
## horsepower76:weight -2.416e-02 9.457e-02 -0.255 0.79892
## horsepower77:weight NA NA NA NA
## horsepower78:weight 1.044e-02 2.263e-02 0.461 0.64560
## horsepower79:weight NA NA NA NA
## horsepower80:weight 2.320e-03 2.227e-02 0.104 0.91725
## horsepower81:weight NA NA NA NA
## horsepower82:weight NA NA NA NA
## horsepower83:weight 5.172e-02 5.269e-02 0.982 0.32873
## horsepower84:weight 2.557e-02 9.183e-02 0.278 0.78126
## horsepower85:weight -8.430e-03 2.090e-02 -0.403 0.68757
## horsepower86:weight 8.641e-03 2.814e-02 0.307 0.75943
## horsepower87:weight NA NA NA NA
## horsepower88:weight -1.692e-03 2.062e-02 -0.082 0.93475
## horsepower89:weight NA NA NA NA
## horsepower90:weight -4.358e-03 2.212e-02 -0.197 0.84427
## horsepower91:weight NA NA NA NA
## horsepower92:weight 2.046e-02 4.034e-02 0.507 0.61320
## horsepower93:weight NA NA NA NA
## horsepower94:weight NA NA NA NA
## horsepower95:weight 6.192e-03 2.126e-02 0.291 0.77150
## horsepower96:weight 3.826e-02 3.282e-02 1.166 0.24662
## horsepower97:weight 2.162e-02 2.612e-02 0.828 0.40984
## horsepower98:weight NA NA NA NA
## horsepower100:acceleration 1.234e-02 2.953e+00 0.004 0.99667
## horsepower102:acceleration NA NA NA NA
## horsepower103:acceleration NA NA NA NA
## horsepower105:acceleration -3.958e-01 2.963e+00 -0.134 0.89401
## horsepower107:acceleration NA NA NA NA
## horsepower108:acceleration NA NA NA NA
## horsepower110:acceleration 1.996e-01 3.064e+00 0.065 0.94818
## horsepower112:acceleration NA NA NA NA
## horsepower113:acceleration NA NA NA NA
## horsepower115:acceleration -1.623e+01 1.783e+01 -0.910 0.36504
## horsepower116:acceleration NA NA NA NA
## horsepower120:acceleration NA NA NA NA
## horsepower122:acceleration NA NA NA NA
## horsepower125:acceleration NA NA NA NA
## horsepower129:acceleration NA NA NA NA
## horsepower130:acceleration -4.823e+00 4.231e+00 -1.140 0.25718
## horsepower132:acceleration NA NA NA NA
## horsepower133:acceleration NA NA NA NA
## horsepower135:acceleration NA NA NA NA
## horsepower137:acceleration NA NA NA NA
## horsepower138:acceleration NA NA NA NA
## horsepower139:acceleration NA NA NA NA
## horsepower140:acceleration -1.132e+00 3.353e+00 -0.338 0.73638
## horsepower142:acceleration NA NA NA NA
## horsepower145:acceleration 1.941e-01 3.541e+00 0.055 0.95641
## horsepower148:acceleration NA NA NA NA
## horsepower149:acceleration NA NA NA NA
## horsepower150:acceleration -9.445e-01 3.159e+00 -0.299 0.76563
## horsepower152:acceleration NA NA NA NA
## horsepower153:acceleration NA NA NA NA
## horsepower155:acceleration NA NA NA NA
## horsepower158:acceleration NA NA NA NA
## horsepower160:acceleration NA NA NA NA
## horsepower165:acceleration 1.684e+01 5.442e+01 0.309 0.75763
## horsepower167:acceleration NA NA NA NA
## horsepower170:acceleration 2.098e+00 1.078e+01 0.195 0.84615
## horsepower175:acceleration 1.134e+00 3.641e+00 0.311 0.75616
## horsepower180:acceleration -2.759e+00 5.587e+00 -0.494 0.62261
## horsepower190:acceleration NA NA NA NA
## horsepower193:acceleration NA NA NA NA
## horsepower198:acceleration NA NA NA NA
## horsepower200:acceleration NA NA NA NA
## horsepower208:acceleration NA NA NA NA
## horsepower210:acceleration NA NA NA NA
## horsepower215:acceleration NA NA NA NA
## horsepower220:acceleration NA NA NA NA
## horsepower225:acceleration -2.020e+00 6.019e+00 -0.336 0.73794
## horsepower230:acceleration NA NA NA NA
## horsepower46:acceleration NA NA NA NA
## horsepower48:acceleration 4.152e+00 6.864e+00 0.605 0.54671
## horsepower49:acceleration NA NA NA NA
## horsepower52:acceleration -8.835e+00 1.000e+01 -0.883 0.37923
## horsepower53:acceleration 1.898e+01 3.167e+01 0.599 0.55050
## horsepower54:acceleration NA NA NA NA
## horsepower58:acceleration NA NA NA NA
## horsepower60:acceleration 5.342e+01 3.557e+01 1.502 0.13644
## horsepower61:acceleration NA NA NA NA
## horsepower62:acceleration NA NA NA NA
## horsepower63:acceleration NA NA NA NA
## horsepower64:acceleration NA NA NA NA
## horsepower65:acceleration -2.099e+00 3.217e+00 -0.653 0.51561
## horsepower66:acceleration NA NA NA NA
## horsepower67:acceleration -4.846e+00 3.454e+00 -1.403 0.16395
## horsepower68:acceleration 2.003e+00 3.367e+00 0.595 0.55330
## horsepower69:acceleration NA NA NA NA
## horsepower70:acceleration 9.337e-01 2.811e+00 0.332 0.74052
## horsepower71:acceleration 3.975e+00 8.327e+00 0.477 0.63423
## horsepower72:acceleration 3.233e-01 2.917e+00 0.111 0.91200
## horsepower74:acceleration NA NA NA NA
## horsepower75:acceleration -6.320e-01 3.162e+00 -0.200 0.84202
## horsepower76:acceleration NA NA NA NA
## horsepower77:acceleration NA NA NA NA
## horsepower78:acceleration -5.101e-01 4.049e+00 -0.126 0.90001
## horsepower79:acceleration NA NA NA NA
## horsepower80:acceleration 1.240e-01 3.069e+00 0.040 0.96786
## horsepower81:acceleration NA NA NA NA
## horsepower82:acceleration NA NA NA NA
## horsepower83:acceleration 1.862e+00 3.596e+00 0.518 0.60582
## horsepower84:acceleration -8.186e-01 5.180e+00 -0.158 0.87477
## horsepower85:acceleration -1.048e+00 2.991e+00 -0.350 0.72681
## horsepower86:acceleration 3.345e-01 2.897e+00 0.115 0.90834
## horsepower87:acceleration NA NA NA NA
## horsepower88:acceleration -1.046e+00 2.956e+00 -0.354 0.72423
## horsepower89:acceleration NA NA NA NA
## horsepower90:acceleration 4.018e-01 2.786e+00 0.144 0.88565
## horsepower91:acceleration NA NA NA NA
## horsepower92:acceleration -5.828e+00 5.576e+00 -1.045 0.29860
## horsepower93:acceleration NA NA NA NA
## horsepower94:acceleration NA NA NA NA
## horsepower95:acceleration 5.476e-01 2.904e+00 0.189 0.85081
## horsepower96:acceleration NA NA NA NA
## horsepower97:acceleration -1.075e+00 3.782e+00 -0.284 0.77689
## horsepower98:acceleration NA NA NA NA
## horsepower100:year -6.954e-01 8.333e-01 -0.834 0.40613
## horsepower102:year NA NA NA NA
## horsepower103:year NA NA NA NA
## horsepower105:year -2.564e-01 7.527e-01 -0.341 0.73418
## horsepower107:year NA NA NA NA
## horsepower108:year NA NA NA NA
## horsepower110:year -3.447e-01 7.394e-01 -0.466 0.64215
## horsepower112:year NA NA NA NA
## horsepower113:year NA NA NA NA
## horsepower115:year NA NA NA NA
## horsepower116:year NA NA NA NA
## horsepower120:year NA NA NA NA
## horsepower122:year NA NA NA NA
## horsepower125:year NA NA NA NA
## horsepower129:year NA NA NA NA
## horsepower130:year 1.108e+00 1.244e+00 0.891 0.37505
## horsepower132:year NA NA NA NA
## horsepower133:year NA NA NA NA
## horsepower135:year NA NA NA NA
## horsepower137:year NA NA NA NA
## horsepower138:year NA NA NA NA
## horsepower139:year NA NA NA NA
## horsepower140:year 8.780e-01 1.254e+00 0.700 0.48566
## horsepower142:year NA NA NA NA
## horsepower145:year -6.692e-01 1.213e+00 -0.552 0.58256
## horsepower148:year NA NA NA NA
## horsepower149:year NA NA NA NA
## horsepower150:year -7.841e-02 8.186e-01 -0.096 0.92389
## horsepower152:year NA NA NA NA
## horsepower153:year NA NA NA NA
## horsepower155:year NA NA NA NA
## horsepower158:year NA NA NA NA
## horsepower160:year NA NA NA NA
## horsepower165:year NA NA NA NA
## horsepower167:year NA NA NA NA
## horsepower170:year 5.960e-01 1.906e+00 0.313 0.75521
## horsepower175:year -8.628e-01 3.595e+00 -0.240 0.81087
## horsepower180:year 1.276e+00 1.188e+00 1.074 0.28542
## horsepower190:year NA NA NA NA
## horsepower193:year NA NA NA NA
## horsepower198:year NA NA NA NA
## horsepower200:year NA NA NA NA
## horsepower208:year NA NA NA NA
## horsepower210:year NA NA NA NA
## horsepower215:year NA NA NA NA
## horsepower220:year NA NA NA NA
## horsepower225:year NA NA NA NA
## horsepower230:year NA NA NA NA
## horsepower46:year NA NA NA NA
## horsepower48:year NA NA NA NA
## horsepower49:year NA NA NA NA
## horsepower52:year NA NA NA NA
## horsepower53:year NA NA NA NA
## horsepower54:year NA NA NA NA
## horsepower58:year NA NA NA NA
## horsepower60:year 2.423e+01 1.561e+01 1.552 0.12396
## horsepower61:year NA NA NA NA
## horsepower62:year NA NA NA NA
## horsepower63:year NA NA NA NA
## horsepower64:year NA NA NA NA
## horsepower65:year 3.560e-01 1.215e+00 0.293 0.77011
## horsepower66:year NA NA NA NA
## horsepower67:year -2.038e+00 8.229e-01 -2.477 0.01503 *
## horsepower68:year -7.474e+00 3.231e+00 -2.313 0.02289 *
## horsepower69:year NA NA NA NA
## horsepower70:year -8.037e-01 7.300e-01 -1.101 0.27365
## horsepower71:year -6.422e-01 1.602e+00 -0.401 0.68935
## horsepower72:year -2.023e+00 1.498e+00 -1.351 0.18002
## horsepower74:year NA NA NA NA
## horsepower75:year -3.062e-01 6.715e-01 -0.456 0.64947
## horsepower76:year NA NA NA NA
## horsepower77:year NA NA NA NA
## horsepower78:year 3.401e-01 1.046e+00 0.325 0.74581
## horsepower79:year NA NA NA NA
## horsepower80:year -7.409e-01 8.311e-01 -0.891 0.37492
## horsepower81:year NA NA NA NA
## horsepower82:year NA NA NA NA
## horsepower83:year NA NA NA NA
## horsepower84:year 1.631e+00 2.197e+00 0.742 0.45967
## horsepower85:year -6.066e-02 6.780e-01 -0.089 0.92890
## horsepower86:year -7.022e-02 1.092e+00 -0.064 0.94885
## horsepower87:year NA NA NA NA
## horsepower88:year -3.455e-01 5.134e-01 -0.673 0.50255
## horsepower89:year NA NA NA NA
## horsepower90:year -6.671e-01 6.674e-01 -0.999 0.32012
## horsepower91:year NA NA NA NA
## horsepower92:year -2.782e-01 2.233e+00 -0.125 0.90112
## horsepower93:year NA NA NA NA
## horsepower94:year NA NA NA NA
## horsepower95:year -1.187e+00 6.098e-01 -1.946 0.05462 .
## horsepower96:year NA NA NA NA
## horsepower97:year NA NA NA NA
## horsepower98:year NA NA NA NA
## horsepower100:origin 1.126e+01 6.084e+00 1.850 0.06737 .
## horsepower102:origin NA NA NA NA
## horsepower103:origin NA NA NA NA
## horsepower105:origin NA NA NA NA
## horsepower107:origin NA NA NA NA
## horsepower108:origin NA NA NA NA
## horsepower110:origin 6.518e+00 7.258e+00 0.898 0.37148
## horsepower112:origin NA NA NA NA
## horsepower113:origin NA NA NA NA
## horsepower115:origin NA NA NA NA
## horsepower116:origin NA NA NA NA
## horsepower120:origin NA NA NA NA
## horsepower122:origin NA NA NA NA
## horsepower125:origin NA NA NA NA
## horsepower129:origin NA NA NA NA
## horsepower130:origin NA NA NA NA
## horsepower132:origin NA NA NA NA
## horsepower133:origin NA NA NA NA
## horsepower135:origin NA NA NA NA
## horsepower137:origin NA NA NA NA
## horsepower138:origin NA NA NA NA
## horsepower139:origin NA NA NA NA
## horsepower140:origin NA NA NA NA
## horsepower142:origin NA NA NA NA
## horsepower145:origin NA NA NA NA
## horsepower148:origin NA NA NA NA
## horsepower149:origin NA NA NA NA
## horsepower150:origin NA NA NA NA
## horsepower152:origin NA NA NA NA
## horsepower153:origin NA NA NA NA
## horsepower155:origin NA NA NA NA
## horsepower158:origin NA NA NA NA
## horsepower160:origin NA NA NA NA
## horsepower165:origin NA NA NA NA
## horsepower167:origin NA NA NA NA
## horsepower170:origin NA NA NA NA
## horsepower175:origin NA NA NA NA
## horsepower180:origin NA NA NA NA
## horsepower190:origin NA NA NA NA
## horsepower193:origin NA NA NA NA
## horsepower198:origin NA NA NA NA
## horsepower200:origin NA NA NA NA
## horsepower208:origin NA NA NA NA
## horsepower210:origin NA NA NA NA
## horsepower215:origin NA NA NA NA
## horsepower220:origin NA NA NA NA
## horsepower225:origin NA NA NA NA
## horsepower230:origin NA NA NA NA
## horsepower46:origin NA NA NA NA
## horsepower48:origin NA NA NA NA
## horsepower49:origin NA NA NA NA
## horsepower52:origin NA NA NA NA
## horsepower53:origin NA NA NA NA
## horsepower54:origin NA NA NA NA
## horsepower58:origin NA NA NA NA
## horsepower60:origin NA NA NA NA
## horsepower61:origin NA NA NA NA
## horsepower62:origin NA NA NA NA
## horsepower63:origin NA NA NA NA
## horsepower64:origin NA NA NA NA
## horsepower65:origin 2.848e+00 6.803e+00 0.419 0.67641
## horsepower66:origin NA NA NA NA
## horsepower67:origin 2.719e+01 7.465e+00 3.642 0.00044 ***
## horsepower68:origin 7.419e+00 5.084e+00 1.459 0.14785
## horsepower69:origin NA NA NA NA
## horsepower70:origin 6.839e+00 5.278e+00 1.296 0.19819
## horsepower71:origin NA NA NA NA
## horsepower72:origin NA NA NA NA
## horsepower74:origin NA NA NA NA
## horsepower75:origin 7.355e+00 4.596e+00 1.600 0.11284
## horsepower76:origin NA NA NA NA
## horsepower77:origin NA NA NA NA
## horsepower78:origin NA NA NA NA
## horsepower79:origin NA NA NA NA
## horsepower80:origin 5.871e+00 1.160e+01 0.506 0.61406
## horsepower81:origin NA NA NA NA
## horsepower82:origin NA NA NA NA
## horsepower83:origin NA NA NA NA
## horsepower84:origin NA NA NA NA
## horsepower85:origin NA NA NA NA
## horsepower86:origin NA NA NA NA
## horsepower87:origin NA NA NA NA
## horsepower88:origin 6.744e+00 5.202e+00 1.296 0.19798
## horsepower89:origin NA NA NA NA
## horsepower90:origin 7.298e+00 5.105e+00 1.430 0.15608
## horsepower91:origin NA NA NA NA
## horsepower92:origin 6.428e+00 1.560e+01 0.412 0.68116
## horsepower93:origin NA NA NA NA
## horsepower94:origin NA NA NA NA
## horsepower95:origin 9.668e+00 5.287e+00 1.829 0.07060 .
## horsepower96:origin NA NA NA NA
## horsepower97:origin NA NA NA NA
## horsepower98:origin NA NA NA NA
## weight:acceleration 8.711e-04 5.749e-04 1.515 0.13303
## weight:year -6.974e-04 4.908e-04 -1.421 0.15862
## weight:origin 6.247e-03 4.270e-03 1.463 0.14678
## acceleration:year 1.038e-01 6.789e-02 1.529 0.12970
## acceleration:origin 4.422e-01 4.026e-01 1.098 0.27489
## year:origin 3.657e-02 2.517e-01 0.145 0.88477
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.201 on 95 degrees of freedom
## Multiple R-squared: 0.981, Adjusted R-squared: 0.9209
## F-statistic: 16.31 on 301 and 95 DF, p-value: < 2.2e-16#f)
y4<-lm(mpg~weight+I((weight)^2),Auto)
summary(y4)##
## Call:
## lm(formula = mpg ~ weight + I((weight)^2), data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.6632 -2.7081 -0.3426 1.8221 16.0931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.256e+01 2.978e+00 21.007 < 2e-16 ***
## weight -1.867e-02 1.964e-03 -9.508 < 2e-16 ***
## I((weight)^2) 1.721e-06 3.050e-07 5.645 3.17e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.19 on 394 degrees of freedom
## Multiple R-squared: 0.7148, Adjusted R-squared: 0.7134
## F-statistic: 493.9 on 2 and 394 DF, p-value: < 2.2e-16plot(y4)
Problem 10
This question should be answered using the Carseats data set.
Fit a multiple regression model to predict Sales using Price, Urban, and US.
Provide an interpretation of each coefficient in the model. Be careful-some of the variables in the model are qualitative!
Write out the model in equation form, being careful to handle the qualitative variables properly.
For which of the predictors can you reject the null hypothesis H0 : ??j = 0?
On the basis of your response to the previous question, fit a smaller model that only uses the predictors for which there is evidence of association with the outcome.
How well do the models in (a) and (e) fit the data?
Using the model from (e), obtain 95% confidence intervals for the coefficient(s).
Is there evidence of outliers or high leverage observations in the model from (e)?
#a
sales<-lm(Sales~Price+Urban+US,data=Carseats)
summary(sales)##
## Call:
## lm(formula = Sales ~ Price + Urban + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9206 -1.6220 -0.0564 1.5786 7.0581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.043469 0.651012 20.036 < 2e-16 ***
## Price -0.054459 0.005242 -10.389 < 2e-16 ***
## UrbanYes -0.021916 0.271650 -0.081 0.936
## USYes 1.200573 0.259042 4.635 4.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.472 on 396 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2335
## F-statistic: 41.52 on 3 and 396 DF, p-value: < 2.2e-16#b
# Price is a continuous variable where one unit increases in price there is a change in sales of -0.54459 units.
# Urban is a categorical variable but the data shows there is no relationship between the sales and the store by looking at the p-value.
# US is categorical where the change in sales is 1.200573.
#c)
#Sales=13.043469 - 0.054459*(Price) - (0.021916)*(1 ,if Urban is Yes 0 if not yes) + 1.200573 (1,if US is Yes 0 if not yes)
#d)
#The null hypothesis can be rejected for Price and UrbanYes as both have p-values less than 0.05.
#e)
sales_var<-lm(Sales~Price+US,data=Carseats)
summary(sales_var)##
## Call:
## lm(formula = Sales ~ Price + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9269 -1.6286 -0.0574 1.5766 7.0515
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.03079 0.63098 20.652 < 2e-16 ***
## Price -0.05448 0.00523 -10.416 < 2e-16 ***
## USYes 1.19964 0.25846 4.641 4.71e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.469 on 397 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2354
## F-statistic: 62.43 on 2 and 397 DF, p-value: < 2.2e-16#f)
anova(sales,sales_var)## Analysis of Variance Table
##
## Model 1: Sales ~ Price + Urban + US
## Model 2: Sales ~ Price + US
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 396 2420.8
## 2 397 2420.9 -1 -0.03979 0.0065 0.9357# The ANOVA test showed that the difference is not statistically significant for either. This causes us to not reject the hypothesis.
#g)
confint(sales_var)## 2.5 % 97.5 %
## (Intercept) 11.79032020 14.27126531
## Price -0.06475984 -0.04419543
## USYes 0.69151957 1.70776632#Using the confidence Interval test we can see that there is a 95% chance that the true parameter for Price falls within the in interval: (-0.0648, -0.0442), and a 5% probability that it doesn’t fall within that interval.
#h)
plot(predict(sales_var),rstudent(sales_var))
lev<-hat(model.matrix(sales_var))
plot(lev)
4/nrow(Carseats)## [1] 0.01plot(Carseats$Sales,Carseats$Price)
points(Carseats[lev>0.01,]$Sales,Carseats[lev>0.01,]$Price,col='red')
Problem 12
This problem involves simple linear regression without an intercept.
Recall that the coefficient estimate ^ ?? for the linear regression of Y onto X without an intercept is given by (3.38). Under what circumstance is the coefficient estimate for the regression of X onto Y the same as the coefficient estimate for the regression of Y onto X?
Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is different from the coefficient estimate for the regression of Y onto X.
Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is the same as the coefficient estimate for the regression of Y onto X.
#a)
#From the equation, the parameter estimate will be equal if the summation of xi^2 equals the summation of yi ^2.
#b)
x=rnorm(100)
y=rbinom(100,2,0.3)
eg<-lm(y~x+0)
summary(eg)##
## Call:
## lm(formula = y ~ x + 0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.28250 0.02498 0.81088 1.01417 2.05525
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## x 0.13892 0.09653 1.439 0.153
##
## Residual standard error: 0.8785 on 99 degrees of freedom
## Multiple R-squared: 0.02049, Adjusted R-squared: 0.0106
## F-statistic: 2.071 on 1 and 99 DF, p-value: 0.1533eg1<-lm(x~y+0)
summary(eg1)##
## Call:
## lm(formula = x ~ y + 0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.49468 -0.56140 -0.07952 0.72266 2.21347
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## y 0.1475 0.1025 1.439 0.153
##
## Residual standard error: 0.9052 on 99 degrees of freedom
## Multiple R-squared: 0.02049, Adjusted R-squared: 0.0106
## F-statistic: 2.071 on 1 and 99 DF, p-value: 0.1533#c)
x=1:100
y=100:1
eg3<-lm(y~x+0)
summary(eg3)##
## Call:
## lm(formula = y ~ x + 0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49.75 -12.44 24.87 62.18 99.49
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## x 0.5075 0.0866 5.86 6.09e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 50.37 on 99 degrees of freedom
## Multiple R-squared: 0.2575, Adjusted R-squared: 0.25
## F-statistic: 34.34 on 1 and 99 DF, p-value: 6.094e-08eg4<-lm(x~y+0)
summary(eg4)##
## Call:
## lm(formula = x ~ y + 0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49.75 -12.44 24.87 62.18 99.49
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## y 0.5075 0.0866 5.86 6.09e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 50.37 on 99 degrees of freedom
## Multiple R-squared: 0.2575, Adjusted R-squared: 0.25
## F-statistic: 34.34 on 1 and 99 DF, p-value: 6.094e-08