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plot(cars)

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head(mtcars)

library(data.table)
library(readr)
library(readxl)
library(ggplot2)
library(ggmosaic)
library(GGally)

Registered S3 method overwritten by 'GGally':
  method from   
  +.gg   ggplot2

Attaching package: ‘GGally’

The following object is masked from ‘package:ggmosaic’:

    happy

library(corrplot)

corrplot 0.94 loaded

library(car)

Loading required package: carData

setdir <- "C:/Users/Risky's/Documents/R/R Notebook/mtcars/"
fwrite(mtcars, paste0(setdir, "mtcars.csv"))

str(dt_mtcars)

Classes ‘data.table’ and 'data.frame':  32 obs. of  11 variables:
 $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
 $ cyl : int  6 6 4 6 8 6 8 4 4 6 ...
 $ disp: num  160 160 108 258 360 ...
 $ hp  : int  110 110 93 110 175 105 245 62 95 123 ...
 $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
 $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
 $ qsec: num  16.5 17 18.6 19.4 17 ...
 $ vs  : int  0 0 1 1 0 1 0 1 1 1 ...
 $ am  : int  1 1 1 0 0 0 0 0 0 0 ...
 $ gear: int  4 4 4 3 3 3 3 4 4 4 ...
 $ carb: int  4 4 1 1 2 1 4 2 2 4 ...
 - attr(*, ".internal.selfref")=<externalptr> 

summary(dt_mtcars)

      mpg             cyl             disp             hp             drat      
 Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0   Min.   :2.760  
 1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5   1st Qu.:3.080  
 Median :19.20   Median :6.000   Median :196.3   Median :123.0   Median :3.695  
 Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7   Mean   :3.597  
 3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0   3rd Qu.:3.920  
 Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0   Max.   :4.930  
       wt             qsec             vs               am              gear      
 Min.   :1.513   Min.   :14.50   Min.   :0.0000   Min.   :0.0000   Min.   :3.000  
 1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:3.000  
 Median :3.325   Median :17.71   Median :0.0000   Median :0.0000   Median :4.000  
 Mean   :3.217   Mean   :17.85   Mean   :0.4375   Mean   :0.4062   Mean   :3.688  
 3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:4.000  
 Max.   :5.424   Max.   :22.90   Max.   :1.0000   Max.   :1.0000   Max.   :5.000  
      carb      
 Min.   :1.000  
 1st Qu.:2.000  
 Median :2.000  
 Mean   :2.812  
 3rd Qu.:4.000  
 Max.   :8.000  

dim(dt_mtcars)

[1] 32 11

quantile(dt_mtcars [, wt])

     0%     25%     50%     75%    100% 
1.51300 2.58125 3.32500 3.61000 5.42400 

print(summary(dt_mtcars))

      mpg             cyl             disp      
 Min.   :10.40   Min.   :4.000   Min.   : 71.1  
 1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8  
 Median :19.20   Median :6.000   Median :196.3  
 Mean   :20.09   Mean   :6.188   Mean   :230.7  
 3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0  
 Max.   :33.90   Max.   :8.000   Max.   :472.0  
       hp             drat             wt       
 Min.   : 52.0   Min.   :2.760   Min.   :1.513  
 1st Qu.: 96.5   1st Qu.:3.080   1st Qu.:2.581  
 Median :123.0   Median :3.695   Median :3.325  
 Mean   :146.7   Mean   :3.597   Mean   :3.217  
 3rd Qu.:180.0   3rd Qu.:3.920   3rd Qu.:3.610  
 Max.   :335.0   Max.   :4.930   Max.   :5.424  
      qsec             vs               am        
 Min.   :14.50   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:16.89   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :17.71   Median :0.0000   Median :0.0000  
 Mean   :17.85   Mean   :0.4375   Mean   :0.4062  
 3rd Qu.:18.90   3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :22.90   Max.   :1.0000   Max.   :1.0000  
      gear            carb      
 Min.   :3.000   Min.   :1.000  
 1st Qu.:3.000   1st Qu.:2.000  
 Median :4.000   Median :2.000  
 Mean   :3.688   Mean   :2.812  
 3rd Qu.:4.000   3rd Qu.:4.000  
 Max.   :5.000   Max.   :8.000  

print(colSums(is.na(dt_mtcars)))

 mpg  cyl disp   hp drat   wt qsec   vs   am gear 
   0    0    0    0    0    0    0    0    0    0 
carb 
   0 

ggpairs(dt_mtcars)

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cor(dt_mtcars [,.(mpg,disp,wt)])

            mpg       disp         wt
mpg   1.0000000 -0.8475514 -0.8676594
disp -0.8475514  1.0000000  0.8879799
wt   -0.8676594  0.8879799  1.0000000

cor(dt_mtcars [, 1:11])

            mpg        cyl       disp         hp        drat         wt        qsec         vs
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684  0.68117191 -0.8676594  0.41868403  0.6640389
cyl  -0.8521620  1.0000000  0.9020329  0.8324475 -0.69993811  0.7824958 -0.59124207 -0.8108118
disp -0.8475514  0.9020329  1.0000000  0.7909486 -0.71021393  0.8879799 -0.43369788 -0.7104159
hp   -0.7761684  0.8324475  0.7909486  1.0000000 -0.44875912  0.6587479 -0.70822339 -0.7230967
drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.00000000 -0.7124406  0.09120476  0.4402785
wt   -0.8676594  0.7824958  0.8879799  0.6587479 -0.71244065  1.0000000 -0.17471588 -0.5549157
qsec  0.4186840 -0.5912421 -0.4336979 -0.7082234  0.09120476 -0.1747159  1.00000000  0.7445354
vs    0.6640389 -0.8108118 -0.7104159 -0.7230967  0.44027846 -0.5549157  0.74453544  1.0000000
am    0.5998324 -0.5226070 -0.5912270 -0.2432043  0.71271113 -0.6924953 -0.22986086  0.1683451
gear  0.4802848 -0.4926866 -0.5555692 -0.1257043  0.69961013 -0.5832870 -0.21268223  0.2060233
carb -0.5509251  0.5269883  0.3949769  0.7498125 -0.09078980  0.4276059 -0.65624923 -0.5696071
              am       gear        carb
mpg   0.59983243  0.4802848 -0.55092507
cyl  -0.52260705 -0.4926866  0.52698829
disp -0.59122704 -0.5555692  0.39497686
hp   -0.24320426 -0.1257043  0.74981247
drat  0.71271113  0.6996101 -0.09078980
wt   -0.69249526 -0.5832870  0.42760594
qsec -0.22986086 -0.2126822 -0.65624923
vs    0.16834512  0.2060233 -0.56960714
am    1.00000000  0.7940588  0.05753435
gear  0.79405876  1.0000000  0.27407284
carb  0.05753435  0.2740728  1.00000000

#Simple Regression Dependent Variable = mpg Independent Variable = am (transmisi) To investigate if transmission (auto=0, manual=1) is significant variable/predictor of miles per gallon (mpg) H0 : There is no significant difference between mpg and am H1 : There is a significant difference between mpg and am

shapiro.test(dt_mtcars [, mpg])

    Shapiro-Wilk normality test

data:  dt_mtcars[, mpg]
W = 0.94756, p-value = 0.1229

Null Hypothesis p < 0.05

t.test(mpg ~am, data= dt_mtcars)

    Welch Two Sample t-test

data:  mpg by am
t = -3.7671, df = 18.332, p-value = 0.001374
alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
95 percent confidence interval:
 -11.280194  -3.209684
sample estimates:
mean in group 0 mean in group 1 
       17.14737        24.39231 

p = 0,001374 < p = 0,05

#Simple Linear Regression

simregression <- lm(mpg ~ am, data= dt_mtcars)
summary(simregression)

Call:
lm(formula = mpg ~ am, data = dt_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-9.3923 -3.0923 -0.2974  3.2439  9.5077 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   17.147      1.125  15.247 1.13e-15 ***
am             7.245      1.764   4.106 0.000285 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.902 on 30 degrees of freedom
Multiple R-squared:  0.3598,    Adjusted R-squared:  0.3385 
F-statistic: 16.86 on 1 and 30 DF,  p-value: 0.000285

summary(simregression2)

Call:
lm(formula = mpg ~ cyl, data = dt_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.9814 -2.1185  0.2217  1.0717  7.5186 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  37.8846     2.0738   18.27  < 2e-16 ***
cyl          -2.8758     0.3224   -8.92 6.11e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.206 on 30 degrees of freedom
Multiple R-squared:  0.7262,    Adjusted R-squared:  0.7171 
F-statistic: 79.56 on 1 and 30 DF,  p-value: 6.113e-10

simregression3 <- lm(mpg ~ as.factor(cyl), data=dt_mtcars )
summary(simregression3)

Call:
lm(formula = mpg ~ as.factor(cyl), data = dt_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.2636 -1.8357  0.0286  1.3893  7.2364 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)      26.6636     0.9718  27.437  < 2e-16 ***
as.factor(cyl)6  -6.9208     1.5583  -4.441 0.000119 ***
as.factor(cyl)8 -11.5636     1.2986  -8.905 8.57e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.223 on 29 degrees of freedom
Multiple R-squared:  0.7325,    Adjusted R-squared:  0.714 
F-statistic:  39.7 on 2 and 29 DF,  p-value: 4.979e-09

dt_mtcars [, cyl6 := as.integer (ifelse(cyl==6, 1,0))]
dt_mtcars [, cyl8 := as.integer (ifelse(cyl==8, 1,0))]
dt_mtcars

summary(simregression4)

Call:
lm(formula = mpg ~ cyl6 + cyl8, data = dt_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.2636 -1.8357  0.0286  1.3893  7.2364 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  26.6636     0.9718  27.437  < 2e-16 ***
cyl6         -6.9208     1.5583  -4.441 0.000119 ***
cyl8        -11.5636     1.2986  -8.905 8.57e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.223 on 29 degrees of freedom
Multiple R-squared:  0.7325,    Adjusted R-squared:  0.714 
F-statistic:  39.7 on 2 and 29 DF,  p-value: 4.979e-09

#MULTIPLE LINEAR REGRESSION

multiregression <- lm(mpg ~ ., data = dt_mtcars)
summary(multiregression)

Call:
lm(formula = mpg ~ ., data = dt_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.4506 -1.6044 -0.1196  1.2193  4.6271 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) 12.30337   18.71788   0.657   0.5181  
cyl         -0.11144    1.04502  -0.107   0.9161  
disp         0.01334    0.01786   0.747   0.4635  
hp          -0.02148    0.02177  -0.987   0.3350  
drat         0.78711    1.63537   0.481   0.6353  
wt          -3.71530    1.89441  -1.961   0.0633 .
qsec         0.82104    0.73084   1.123   0.2739  
vs           0.31776    2.10451   0.151   0.8814  
am           2.52023    2.05665   1.225   0.2340  
gear         0.65541    1.49326   0.439   0.6652  
carb        -0.19942    0.82875  -0.241   0.8122  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.65 on 21 degrees of freedom
Multiple R-squared:  0.869, Adjusted R-squared:  0.8066 
F-statistic: 13.93 on 10 and 21 DF,  p-value: 3.793e-07

back_multiregression <- step(multiregression, direction ="backward", trace = FALSE)
summary(back_multiregression)

Call:
lm(formula = mpg ~ wt + qsec + am, data = dt_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.4811 -1.5555 -0.7257  1.4110  4.6610 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   9.6178     6.9596   1.382 0.177915    
wt           -3.9165     0.7112  -5.507 6.95e-06 ***
qsec          1.2259     0.2887   4.247 0.000216 ***
am            2.9358     1.4109   2.081 0.046716 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.459 on 28 degrees of freedom
Multiple R-squared:  0.8497,    Adjusted R-squared:  0.8336 
F-statistic: 52.75 on 3 and 28 DF,  p-value: 1.21e-11

par (mfrow = c(2,2))
plot(back_multiregression)

new_mtcars$cyl <- as.factor(new_mtcars$cyl)
new_mtcars$gear <- as.factor(new_mtcars$gear)
new_mtcars$carb <- as.factor(new_mtcars$carb)
new_mtcars$am <- as.factor(new_mtcars$am)
new_mtcars$vs <- as.factor(new_mtcars$vs)

#Plot mpg, wt & vs

ggplot(new_mtcars, aes(x=wt, y=mpg, color=vs)) + geom_smooth() + geom_point() + labs(x="Weight", y="Miles/gallon", color="Engine (0=V-Shaped,1=Straight)")

`geom_smooth()` using method = 'loess' and formula = 'y ~ x'

summary(multiregression2)

Call:
lm(formula = mpg ~ ., data = new_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5087 -1.3584 -0.0948  0.7745  4.6251 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) 23.87913   20.06582   1.190   0.2525  
cyl6        -2.64870    3.04089  -0.871   0.3975  
cyl8        -0.33616    7.15954  -0.047   0.9632  
disp         0.03555    0.03190   1.114   0.2827  
hp          -0.07051    0.03943  -1.788   0.0939 .
drat         1.18283    2.48348   0.476   0.6407  
wt          -4.52978    2.53875  -1.784   0.0946 .
qsec         0.36784    0.93540   0.393   0.6997  
vs1          1.93085    2.87126   0.672   0.5115  
am1          1.21212    3.21355   0.377   0.7113  
gear4        1.11435    3.79952   0.293   0.7733  
gear5        2.52840    3.73636   0.677   0.5089  
carb2       -0.97935    2.31797  -0.423   0.6787  
carb3        2.99964    4.29355   0.699   0.4955  
carb4        1.09142    4.44962   0.245   0.8096  
carb6        4.47757    6.38406   0.701   0.4938  
carb8        7.25041    8.36057   0.867   0.3995  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.833 on 15 degrees of freedom
Multiple R-squared:  0.8931,    Adjusted R-squared:  0.779 
F-statistic:  7.83 on 16 and 15 DF,  p-value: 0.000124

back_multiregression2 <- step(multiregression2, direction="backward", trace=FALSE)
summary(back_multiregression2)

Call:
lm(formula = mpg ~ cyl + hp + wt + am, data = new_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.9387 -1.2560 -0.4013  1.1253  5.0513 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 33.70832    2.60489  12.940 7.73e-13 ***
cyl6        -3.03134    1.40728  -2.154  0.04068 *  
cyl8        -2.16368    2.28425  -0.947  0.35225    
hp          -0.03211    0.01369  -2.345  0.02693 *  
wt          -2.49683    0.88559  -2.819  0.00908 ** 
am1          1.80921    1.39630   1.296  0.20646    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.41 on 26 degrees of freedom
Multiple R-squared:  0.8659,    Adjusted R-squared:  0.8401 
F-statistic: 33.57 on 5 and 26 DF,  p-value: 1.506e-10

both_multiregression <- stepAIC(multiregression2, direction = "both", trace= FALSE)
summary(both_multiregression)

Call:
lm(formula = mpg ~ cyl + hp + wt + am, data = new_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.9387 -1.2560 -0.4013  1.1253  5.0513 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 33.70832    2.60489  12.940 7.73e-13 ***
cyl6        -3.03134    1.40728  -2.154  0.04068 *  
cyl8        -2.16368    2.28425  -0.947  0.35225    
hp          -0.03211    0.01369  -2.345  0.02693 *  
wt          -2.49683    0.88559  -2.819  0.00908 ** 
am1          1.80921    1.39630   1.296  0.20646    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.41 on 26 degrees of freedom
Multiple R-squared:  0.8659,    Adjusted R-squared:  0.8401 
F-statistic: 33.57 on 5 and 26 DF,  p-value: 1.506e-10

Intepretation: - The intercept represents the average improvement in miles per gallon (mpg) for an automatic car with 4 cylinders, assuming horsepower (hp) and weight (wt) are zero. - Moving from 4 to 6 cylinders decreases mpg by 3.013. - Moving from 4 to 8 cylinders decreases mpg by 2.16. - A 1-unit increase in horsepower(hp) decreases mpg by 0.032. - A 1-unit increase in weight(wt) decreases mpg by 2.5. - Manual transmission increases mpg by 1.809.

# Step 7: Diagnostic plots to check assumptions
par(mfrow = c(2, 2))  # 2x2 plot layout
plot(back_multiregression2)

Here’s a description of the diagnostic plots shown in the image:

1. Residuals vs Fitted (Top Left):

• This plot checks the linearity assumption. Ideally, residuals should be randomly scattered around the horizontal line (y = 0).

  Result : In this case, there seems to be a slight curve, suggesting potential non-linearity or an issue with model fit.

2. Normal Q-Q Plot (Top Right):

• This plot checks if residuals follow a normal distribution. Points should fall along the diagonal line.

  Result : Most points follow the line, but deviations in the tails suggest that the residuals may not be perfectly normally distributed.

3. Scale-Location (Bottom Left):

• This plot tests for homoscedasticity (constant variance of residuals). The residuals should be evenly spread along the fitted values.

  Result : The red line appears fairly flat, but some spread increases on the right side, indicating potential heteroscedasticity (non-constant variance).

4. Residuals vs Leverage (Bottom Right):

• This plot identifies influential points and potential outliers. Points with high leverage and large residuals could disproportionately affect the model.

  Result : A few points, like 17, 18, and 20, are highlighted near Cook’s distance lines, which could indicate influential data points.

Overall, the diagnostic plots suggest that while the model performs reasonably well, there may be concerns regarding non-linearity, potential outliers, and slight heteroscedasticity. Adjustments to the model or further investigation of influential points may be needed.

# Step 8: Check for multicollinearity using VIF (Variance Inflation Factor)
vif(back_multiregression2)

        GVIF Df GVIF^(1/(2*Df))
cyl 5.824545  2        1.553515
hp  4.703625  1        2.168784
wt  4.007113  1        2.001778
am  2.590777  1        1.609589

Calculated the Generalized Variance Inflation Factor (GVIF) for variables to check for multicollinearity. Interpretation of the results:

GVIF: Generalized Variance Inflation Factor, which adjusts for the degrees of freedom (Df). Df: Degrees of freedom for each variable.

Interpretation: cyl: GVIF^(1/(2Df)) = 1.553515 hp: GVIF^(1/(2Df)) = 2.168784 wt: GVIF^(1/(2Df)) = 2.001778 am: GVIF^(1/(2Df)) = 1.609589

Generally, a GVIF^(1/(2*Df)) value greater than 2.5 or 3 indicates potential multicollinearity issues. In this case, none of the variables exceed this threshold, suggesting that multicollinearity is not a significant problem for the model.

# Step 9: Conclusion (print output)
cat("\nBest variables selected for predicting mpg:\n")

Best variables selected for predicting mpg:

print(names(coef(back_multiregression2)))

[1] "(Intercept)" "cyl6"        "cyl8"        "hp"          "wt"          "am1"        

cat("\nModel Summary:\n")

Model Summary:

print(summary(back_multiregression2))

Call:
lm(formula = mpg ~ cyl + hp + wt + am, data = new_mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.9387 -1.2560 -0.4013  1.1253  5.0513 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 33.70832    2.60489  12.940 7.73e-13 ***
cyl6        -3.03134    1.40728  -2.154  0.04068 *  
cyl8        -2.16368    2.28425  -0.947  0.35225    
hp          -0.03211    0.01369  -2.345  0.02693 *  
wt          -2.49683    0.88559  -2.819  0.00908 ** 
am1          1.80921    1.39630   1.296  0.20646    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.41 on 26 degrees of freedom
Multiple R-squared:  0.8659,    Adjusted R-squared:  0.8401 
F-statistic: 33.57 on 5 and 26 DF,  p-value: 1.506e-10

Based on the linear regression model summary, here are the key conclusions:

1. Significant Predictors:

• Cylinders (cyl6): Cars with 6 cylinders have a significant negative impact on miles per gallon (mpg), reducing it by approximately 3.03 units.
• Horsepower (hp): An increase in horsepower is associated with a slight but significant decrease in mpg.
• Weight (wt): Heavier cars tend to have lower mpg, with weight being a significant predictor.

2. Non-Significant Predictors:

• Cylinders (cyl8): Cars with 8 cylinders do not significantly affect mpg in this model.
• Transmission (am1): The type of transmission (manual vs. automatic) does not significantly impact mpg.

3. Model Fit:

• The model explains a substantial portion of the variance in mpg, with an R-squared value of 0.8659. This means approximately 86.59% of the variability in mpg is explained by the model.
• The adjusted R-squared value of 0.8401 indicates a good fit, accounting for the number of predictors in the model.

4. Overall Significance:

• The model is statistically significant overall, with a p-value of 1.506e-10, indicating that the predictors collectively have a significant effect on mpg.

In summary, the model suggests that the number of cylinders (specifically 6 cylinders), horsepower, and weight are significant factors affecting a car’s fuel efficiency, while the type of transmission and having 8 cylinders are not significant predictors in this context. The model fits the data well and explains a large portion of the variability in fuel efficiency.