HW4
Soumya Halder
11/10/2019
Question 1
##
## Call:
## lm(formula = Y ~ X1 + X2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.00 -6.57 -1.95 4.42 24.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.6556 13.5076 2.936 0.005225 **
## X1 0.1662 0.1626 1.022 0.312128
## X2 -1.7021 0.4421 -3.850 0.000371 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.098 on 45 degrees of freedom
## Multiple R-squared: 0.5613, Adjusted R-squared: 0.5418
## F-statistic: 28.79 on 2 and 45 DF, p-value: 8.869e-09
## fit lwr upr
## 1 37.79178 27.08759 48.49596## Installing package into 'C:/Users/sthal/OneDrive/Documents/R/win-library/3.6'
## (as 'lib' is unspecified)## package 'car' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\sthal\AppData\Local\Temp\Rtmpqw6dxM\downloaded_packages## Loading required package: carData## X1 X2
## 2.611671 2.611671Question 2: Simple LR, Y = 10 + 5X - X^2 with only X
##
## Call:
## lm(formula = Y ~ X, data = YDF)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2342 -0.2929 0.1358 0.5694 1.9273
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.5188 0.4870 56.51 <2e-16 ***
## X -6.9848 0.1588 -43.99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8617 on 98 degrees of freedom
## Multiple R-squared: 0.9518, Adjusted R-squared: 0.9513
## F-statistic: 1935 on 1 and 98 DF, p-value: < 2.2e-16
Question 2: Quadratic LR, Y = 10 + 5X - 2X^2 with X^2
##
## Call:
## lm(formula = Y ~ X + XX, data = YDF)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.19046 -0.30582 0.03546 0.31477 1.38463
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.7438 1.0707 10.034 < 2e-16 ***
## X 4.4770 0.7154 6.258 1.06e-08 ***
## XX -1.8949 0.1175 -16.131 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4513 on 97 degrees of freedom
## Multiple R-squared: 0.9869, Adjusted R-squared: 0.9866
## F-statistic: 3656 on 2 and 97 DF, p-value: < 2.2e-16
## X XX
## 73.97863 73.97863Part e: Centering the data
##
## Call:
## lm(formula = Y ~ I(X - mean(X)) + I((X - mean(X))^2), data = YDF)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.19046 -0.30582 0.03546 0.31477 1.38463
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.99386 0.05686 122.99 <2e-16 ***
## I(X - mean(X)) -6.96179 0.08319 -83.69 <2e-16 ***
## I((X - mean(X))^2) -1.89486 0.11747 -16.13 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4513 on 97 degrees of freedom
## Multiple R-squared: 0.9869, Adjusted R-squared: 0.9866
## F-statistic: 3656 on 2 and 97 DF, p-value: < 2.2e-16
## I(X - mean(X)) I((X - mean(X))^2)
## 1.000295 1.000295