For the record, this is a homework question. A statistics student wishes to understand the relationship between a used car's price and the number of miles that car has been driven. The student goes to a local car lot and writes down the prices and the odometer reading for 100 cars. The student takes this information and completes a regression. The goal is to examine how the miles drove impacts the car's price. The regression output appears at the end of this assignment. Use the output to answer the following questions.
a) (3 points) Dependent variables Independent variable
b) (8 points) Do you expect a positive, negative, or no relationship between miles driven and price? Draw a scatterplot that corresponds to your relationship.
Be sure to include which variable (miles or price) is on the x-axis and which is on the y-axis.
b) (3 points) Write the regression equation (I want the specific estimates for the coefficients)
c) (3 points) What is the interpretation of the slope coefficient of b 1 (in terms of this problem)?
d) (4 points) Is b 1 significant from zero? How do you know?
e) (3 points) Use the regression equation to predict the price for a car that was driven for 30,000 miles. Is this mileage appropriate to make a prediction? Why or why not?
f) (3 points) Use the regression equation to predict the price for a car that was driven for 80,000 miles. Is this mileage appropriate to make a prediction? Why or why not?
g) (3 points) What percentage of price variation is explained by the variation in miles driven?
Multiple R 0.398635
R square 0.15891
Adjusted R Squared 0.150327
Standard Error 1481.414
Observations 100
df ss ms f significance f
Regression 1 40633716.14 40633716 18.51542325 3.99E-05
Residual 98 215069573.5 2194587
Total 99 255703289.7
coefficient standard error t stat p value lower 95%
intercept 20261.42 598.0313643 33.8802 6.53E-56 19074.64824
x1 -0.07332 0.017039697 -4.30296 3.99E-05 -0.107135778
Sample range for Y 14281 20511
Sample range for X 19100 49200
For the record, this is a homework question. A statistics student wishes to understand the relationship between a used car's price and the number of miles that car has been driven. The student goes to a local car lot and writes down the prices and the odometer reading for 100 cars. The student takes this information and completes a regression. The goal is to examine how the miles drove impacts the car's price. The regression output appears at the end of this assignment. Use the output to answer the following questions.
a) (3 points) Dependent variables Independent variable
b) (8 points) Do you expect a positive, negative, or no relationship between miles driven and price? Draw a scatterplot that corresponds to your relationship.
Be sure to include which variable (miles or price) is on the x-axis and which is on the y-axis.
b) (3 points) Write the regression equation (I want the specific estimates for the coefficients)
c) (3 points) What is the interpretation of the slope coefficient of b 1 (in terms of this problem)?
d) (4 points) Is b 1 significant from zero? How do you know?
e) (3 points) Use the regression equation to predict the price for a car that was driven for 30,000 miles. Is this mileage appropriate to make a prediction? Why or why not?
f) (3 points) Use the regression equation to predict the price for a car that was driven for 80,000 miles. Is this mileage appropriate to make a prediction? Why or why not?
g) (3 points) What percentage of price variation is explained by the variation in miles driven?
Multiple R 0.398635
R square 0.15891
Adjusted R Squared 0.150327
Standard Error 1481.414
Observations 100
df ss ms f significance f
Regression 1 40633716.14 40633716 18.51542325 3.99E-05
Residual 98 215069573.5 2194587
Total 99 255703289.7
coefficient standard error t stat p value lower 95%
intercept 20261.42 598.0313643 33.8802 6.53E-56 19074.64824
x1 -0.07332 0.017039697 -4.30296 3.99E-05 -0.107135778
Sample range for Y 14281 20511
Sample range for X 19100 49200
