1.Linear regression model with one dependent variable mpg (miles per gallon). This variable describes how many miles a car runs on one gallon of gas. Higher mpg means the car consumes less gas.

The independent variable is "cyl" (number of cylinders in the car's engine). More cylinders means that the car is has more powerful engine.

2. In the second model I add one more independent variable "hp" (horsepower).

QUESTION:

1. Write the estimated equations for both models (the equation of the line for model1 and model2. (50 points)

2. Does the variable "cyl" explain well the variability in "mpg"? explain why. (25 points)

3. Does the variable "hp" explain well the variability in "mpg"? explain why. (25 points)

Linear Regression 1

Call:

lm(formula = mpg ~ cyl, data = 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

Linear Regression 2

lm(formula = mpg ~ cyl + hp, data = mtcars)

Residuals:

Min 1Q Median 3Q Max -4.4948 -2.4901 -0.1828 1.9777 7.2934

Coefficients:

Estimate Std. Error t value Pr(>|t|) (Intercept) 36.90833 2.19080 16.847 < 2e-16 cyl -2.26469 0.57589 -3.933 0.00048 hp -0.01912 0.01500 -1.275 0.21253 ---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.173 on 29 degrees of freedom

Multiple R-squared: 0.7407, Adjusted R-squared: 0.7228

F-statistic: 41.42 on 2 and 29 DF, p-value: 3.162e-09