Question

R programming:

Problem Tw o: a) Create a side-by-side box plot of the variable MPG of the two types of car engines. b) Conduct a two-tailed t-test comparing the average MPG of a V-shaped type of car engine vs the average MPG of a Straight type of car engine. Report your p-value. Conduct a simple linear regression using MPG as your response variable and WT as your predictor. c) d) Create a scatter plot WT vs MPG then plot the least square regression line on the same e Report the summary of your linear model, interpret the slope and the y-intercept in the f) Construct a 95% confidence interval for both: the slope and the y-intercept. graph. model based on the context Using R or a calculator of your choice to calculate SST (total). SSE (residual), SSRegressiom g)

MPG   GPM   WT   DIS   NC   HP   ACC   ET
16.9   5.917   4.360   350   8   155   14.9   1
15.5   6.452   4.054   351   8   142   14.3   1
19.2   5.208   3.605   267   8   125   15.0   1
18.5   5.405   3.940   360   8   150   13.0   1
30.0   3.333   2.155   98   4   68   16.5   0
27.5   3.636   2.560   134   4   95   14.2   0
27.2   3.676   2.300   119   4   97   14.7   0
30.9   3.236   2.230   105   4   75   14.5   0
20.3   4.926   2.830   131   5   103   15.9   0
17.0   5.882   3.140   163   6   125   13.6   0
21.6   4.630   2.795   121   4   115   15.7   0
16.2   6.173   3.410   163   6   133   15.8   0
20.6   4.854   3.380   231   6   105   15.8   0
20.8   4.808   3.070   200   6   85   16.7   0
18.6   5.376   3.620   225   6   110   18.7   0
18.1   5.525   3.410   258   6   120   15.1   0
17.0   5.882   3.840   305   8   130   15.4   1
17.6   5.682   3.725   302   8   129   13.4   1
16.5   6.061   3.955   351   8   138   13.2   1
18.2   5.495   3.830   318   8   135   15.2   1
26.5   3.774   2.585   140   4   88   14.4   0
21.9   4.566   2.910   171   6   109   16.6   1
34.1   2.933   1.975   86   4   65   15.2   0
35.1   2.849   1.915   98   4   80   14.4   0
27.4   3.650   2.670   121   4   80   15.0   0
31.5   3.175   1.990   89   4   71   14.9   0
29.5   3.390   2.135   98   4   68   16.6   0
28.4   3.521   2.670   151   4   90   16.0   0
28.8   3.472   2.595   173   6   115   11.3   1
26.8   3.731   2.700   173   6   115   12.9   1
33.5   2.985   2.556   151   4   90   13.2   0
34.2   2.924   2.200   105   4   70   13.2   0
31.8   3.145   2.020   85   4   65   19.2   0
37.3   2.681   2.130   91   4   69   14.7   0
30.5   3.279   2.190   97   4   78   14.1   0
22.0   4.545   2.815   146   6   97   14.5   0
21.5   4.651   2.600   121   4   110   12.8   0
31.9   3.135   1.925   89   4   71   14.0   0

Answer 1

a)

## To import the dataset select the file after running the below command

data_20Jan = read.csv(file.choose(),header = T)

head(data_20Jan)

# Boxplot of MPG by Car Cylinders

boxplot(MPG~ET,data=data_20Jan, main="Car Milage Data",

        xlab="Car Type", ylab="Miles Per Gallon")

Car Milage Data I) 13 12 0 Car Type

b)

This part cannot be done with the description of the column names of the dataset

c)

#MPG = Y , WT = X

regmodel <- lm(MPG ~ WT, data = data_20Jan)

summary(regmodel)

Output

Call:

lm(formula = MPG ~ WT, data = data_20Jan)

Residuals:

    Min      1Q Median      3Q     Max

-5.4595 -1.9004 0.1686 1.4032 6.4091

Coefficients:

            Estimate Std. Error t value Pr(>|t|)   

(Intercept)   48.708      1.954   24.93 < 2e-16 ***

WT            -8.365      0.663 -12.62 8.89e-15 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.851 on 36 degrees of freedom

Multiple R-squared: 0.8155, Adjusted R-squared: 0.8104

F-statistic: 159.2 on 1 and 36 DF, p-value: 8.889e-15

d)

plot(data_20Jan$WT, data_20Jan$MPG, main="Scatterplot",

     xlab="WT ", ylab="Miles Per Gallon ", pch=19)

# Add fit lines

abline(lm(data_20Jan$MPG~data_20Jan$WT), col="red") # regression line (y~x)

Scatterplot 3.0 3.5 4.0 2.0 2.5 WT

e)

Output

Call:

lm(formula = MPG ~ WT, data = data_20Jan)

Residuals:

    Min      1Q Median      3Q     Max

-5.4595 -1.9004 0.1686 1.4032 6.4091

Coefficients:

            Estimate Std. Error t value Pr(>|t|)   

(Intercept)   48.708      1.954   24.93 < 2e-16 ***

WT            -8.365      0.663 -12.62 8.89e-15 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.851 on 36 degrees of freedom

Multiple R-squared: 0.8155, Adjusted R-squared: 0.8104

F-statistic: 159.2 on 1 and 36 DF, p-value: 8.889e-15

Regression Equation

MPG = 48.708 – 8.365 WT

Interpretation of Slope:

The amount by which the response variable (MPG) increases or decreases, on average, when the explanatory variable (WT) increases by one.

The y intercept is the value at which the fitted line crosses the y-axis. In this case, its value is 48.708. ie when WT is zero, MPG is 48.708 units.

f)

95% CI for Slope = -8.365 +/- 1.96 * 0.663 = {-9.66, -7.07}

95% CI for Intercept = 48.708 +/- 1.96 * 1.954 = {44.88, 52.54}

g)

SS_Regression = 1,293.52

SS_Residual = 292.58

SS_Total = SS_Regression +SS_Residual = 1,586.09