Part $1$

Please use "Auto Data." This dataset includes information about $392$ vehicle types. The task is to find a set of variables and their function forms to predict miles per gallon $($i$.$e$.,$ mpg $).$ The dataset provides the following information $(4$ pts $)$:

Mpg $=$ miles per gallon

origin $=$ Origin of the car. This has three levels $(1.$ American, $2.$ European, $3.$ Japanese$)$

cylinders $=$ Number of cylinders between $4$ and $8$

displacement $=$ Engine displacement $($cu$.$ inches$)$

horsepower $=$ Engine horsepower

weight $=$ Vehicle weight $($lbs$.)$

acceleration $=$ Time to accelerate from $0$ to $60$ mph $($sec$.)$

year $=$ Model year

We are looking for insights from the following analyses:

Check if there is any relationship of mpg with other variables using scatterplots$/$boxplots and correlation. Based on the results, make your inference about the relationship $($i$.$e$.,$ has a relationship, does not have a relationship, highly correlated, etc.$).$ Provide codes.

Estimate a linear regression model and interpret its results $($show estimation codes$).$

Estimate a non$-$linear model with quadratic terms of the displacement, horsepower, weight, along with other variables. Find the minimum$/$optimal values $($if any$)$ for displacement, horsepower, weight. Provide interpretations of estimates of all the variables. $($show estimation codes$).$

Check if the nonlinear model in Q$3$ followed a normal distribution. If yes, provide the proof. $($show estimation codes$).$