Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), the number of doors (Doors), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition.

Determine which major variables are dummies and are dynamic?

Identify 3 potential unobserved heterogenous factors in this dataset.

Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)?

What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” the kurtosis for “doors” and mean for “sound”?

Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test.

Create a red scatterplot matrix of price, mileage, cylinder, liter, doors, make. From your graph, is the correlation between price & mileage positive or negative?

What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “doors” correct to 2 d.p

Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions.

Specify the regression model for the whole data keeping the exact names of the variables.

Write the estimated regression equation.

In one sentence, which variables are significant and which are not? Justify

Is the regression model justifiable? Explain

Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, 4 doors, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, 2 doors, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. 

Which factor(s) appears to be causing a comparative difference (if any)?