1) The following dataset contains data about cars and their prices:

Price is the price of the particular make of a car, mpg stands for miles per gallon, weight is the weight in pounds and domestic/foreign signifies if the car is produced in the US or not.

a) First run a regression, explaining the price of a car by mpg. Help me to write down the regression equation you find. If this relationship significant? What would you expect a car with mpg of 20 to cost according to this analysis?

b) Now run a regression on price with all available variables except make (foreign is not coded correctly for this, as you will see, so you have to recode it to a dummy variable).

i) Is the overall model good or not? How can you tell?

ii) Write down the regression equation for this model and interpret the coefficients as well as the intercept. Is the model better or worse than the model in a)?

c) Multiple assumptions must be fulfilled so that you can interpret the output of a regression in a clear and concise way. The most important ones are the following; find out if these assumptions are violated or not for the model found in b. In case they are, also suggest a possible solution.

i) There is a linear relationship between the dependent and independent variables.

ii) Normal Distribution of Errors

iii) The variance of the errors is constant across the whole spectrum of data; this is called homoscedasticity.

iv) No significant linear relationship between the independent variables (No Multikollinearity).

d) The model found in a) and the model found in b) have different coefficients for mpg, and more importantly, the significance of mpg in the models is different. How can you explain this (based on what you found in c), and in general)?