Variables in the Mtcars Data Set to Use for Modeling Quarter Mile Times Statistics Assignment Help

Assignment Task

Problems to Turn In
1. (a) Perhaps the most obvious predictor among the variables in the mtcars data set to use for modeling quarter mile times is the horsepower of a car. Use R to fit a simple linear regression model of quarter mile times versus horsepower, and give
a single number from the R output that provides confirmation that there is a statistically significant relationship between these two variables. Also, interpret the point estimate of the coefficient of hp.
(b) Another variable that likely has a relationship with quarter mile times is transmission type am, which is encoded as am = 0 for automatic transmissions and am = 1 for manual transmissions (note that this makes am an indicator variable for the category manual). Now we will consider the relationship of transmission type with quarter mile times in cars of a fixed horsepower or after accounting for horsepower (i.e., we have the variable hp in the MLR model in addition to am). Create a scatter plot of Y = qsec versus X = hp with different colors and/or different plotting symbols for automatic cars and manual cars. You can do this by using the col= or pch= options for the plot() function, and supplying a vector of the same length as X and Y that specifies the color or plotting symbol that the corresponding (X, Y ) point should have. Hint: There are lots of ways to create such a vector, but the ifelse() function may prove useful. From your plot, which transmission type appears to have on average faster cars at a fixed level of horsepower (keeping in mind that faster means lower ET’s)?
(c) Fit the multiple linear regression model Yi = ? + ?Xi + ?Di + i of quarter mile time (Y ) versus both horsepower (X) and transmission type (D), and interpret the estimated coefficient ˆ? of the am variable.
(d) Test, using a significance level of ? = 0.01, whether transmission type is related to how quickly cars complete the quarter mile in cars of a fixed horsepower

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