Question

Question 1: Using 1 variable regression house price vs. number of rooms predict the price of a house with 4 rooms for your client.




You enhance the model by adding 2 more variables:

Question 2: What is the predicted house price for a home based on the new model with 3 variables, given that the house has 5 rooms is 10 years old and is 2,000 Square feet?





Question 3: Which coefficients are statistically significant at alpha (α) 5% in the model with 3 variables




Question 4: What is the 95% confidence interval for Square Ft. coefficient?




Question 5: Which of the two models (house price vs. # Rooms or House Price vs. #Rooms, Age and square ft.) will you choose to use and why?



SUMMARY OUTPUT
Regression Statistics Multiple R 0.5996 R Square 0.3595 Adjusted R Square 0.3328
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 50,000 24,200 2.0661 4.93% 159 99,841 # of Rooms 20,000 4,753 4.2079 0.03% 10,212 29,788   
SUMMARY OUTPUT
Regression Statistics Multiple R 0.8131 R Square 0.6611 Adjusted R Square 0.6149
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 45,000 21,780 2.066 4.93% 143 89,857 # of Rooms 200 121 1.656 11.02% (49) 449 Age of House (1,000) 314 (3.183) 0.39% (1,647) (353) Square Ft. 50 17 2.875 0.81% 14 86   

Answer 1

Question 1: Using 1 variable regression house price vs. number of rooms predict the price of a house with 4 rooms for your client.

regression equation/model is

Price=50000+20000*Room

for Room=4, Price=50000+20000*4=130000

answer is 130000

Question 2: What is the predicted house price for a home based on the new model with 3 variables, given that the house has 5 rooms is 10 years old and is 2,000 Square feet?

regression model is

Price=45000+200*Room+1000*Age+50*square_feet

for 5 rooms is 10 years old and is 2,000 Square feet, Price=45000+200*5+1000*10+50*2000=156000

answer is 156000

here please check the sign of the coefficient Age of house, I think it should be negative

Question 3: Which coefficients are statistically significant at alpha (α) 5% in the model with 3 variables

Age_of_house and Square_feet are significant as their p-value is less than alpha=5%

Question 4: What is the 95% confidence interval for Square Ft. coefficient?

confidence interval=(14, 86)

Question 5: Which of the two models (house price vs. # Rooms or House Price vs. #Rooms, Age and square ft.) will you choose to use and why?

second model i.e. House Price vs. #Rooms, Age and square ft

since the R Square 0.6611 Adjusted R Square 0.6149 for this is more than that of first model R Square 0.3595 Adjusted R Square 0.3328