Question

Use the HousePrice data and via multiple regression select the two variables that predict the house selling price the best. Make another table with these two variables and answer the questions. Numerical answers are rounded so choose the answer that matches the best:

9. Identify the negative coefficient. What is its value and what is the interpretation of this number? (Choose the most appropriate answer. Note: numbers are truncated.)

• a. -0.037; This is a negative number and serves no statistical interpretation in this case.
• b. -0.037; This is how much the selling price of the house will decrease in hundred thousand as the house age by a year.
• c. -0.077; This show how much selling price correlates with the age of the house
• d. -1.92; For each additional bathroom the selling price of the house decrease by 1.92 hundred thousand dollars.

10. Which of the two variables has better P-value and what is this P-value? (Note: numbers are truncated.)

• a. Age has the best P-value; P-value = 0.067
• b. The higher the P-value, the better; so a P-value = 1.08E-09 is very good.
• c. #Bathroooms has the best P-value; P-value = 1.08E-09
• d. All P-values are poor since they are allhigher 5%.

11. Using this second table predict the selling price of a housethat is 10 years old, has 2 bathrooms and 3 rooms.

• a. 10.5 hundred thousands
• b. 12.57 hundred thousands
• c. 9.06 hundred thousands
• d. 11.58 hundred thousands

12. Based on the table would you characterize the Regression fit and the prediction as Poor, Good, Very Good, or Excellent?

• a. Poor
• b. Good
• c. Very Good
• d. Excellent

Age     #Bathrooms      #Rooms  #BedRooms       #FirePlaces     sellingPrice in $100000
42      1       7       4       0       4.9176
62      1       7       4       0       5.0208
40      1       6       3       0       4.5429
54      1       6       3       0       4.5573
42      1       6       3       0       5.0597
56      1       6       3       0       3.891
51      1       7       3       1       5.898
32      1       6       3       0       5.6039
32      1       6       3       0       5.8282
30      1       6       3       0       5.3003
30      1       5       2       0       6.2712
32      1       6       3       0       5.9592
32      1       6       3       0       5.6039
50      1.5     8       4       0       8.2464
17      1.5     6       3       0       7.7841
23      1       7       3       0       9.0384
22      1.5     6       3       0       7.5422
44      1.5     6       3       0       6.0931
3       1       7       3       0       8.14
31      1.5     8       4       0       9.1416
42      2.5     10      5       1       16.4202
14      2.5     9       5       1       14.4598
46      1       5       2       1       5.05
22      1.5     7       3       1       6.6969
40      1       6       3       1       5.9894
50      1.5     8       4       1       8.7951
48      1.5     8       4       1       8.3607
30      1.5     6       3       1       12

Answer 1

Regression with all the variables.
Put the data in excel and using the regression under data analysis tab, we input the values

The output is as follows.

Regression with the best two variable
We select the variable based on the pvalue.

For each beta coefficient we test the following hypothesis.

Next we check the pvalue for the variable in the regression output and check if the pvalue is less than 0.05, if it is less than 0.05, then we reject the null hypothesis and conclude that the variable is significant.

We find that only Age and #Bathroom are significant with a pvalue less than 0.05
Hence only these two are select in the next model.

Screenshots of the inputs and the output are shown below.

9. Identify the negative coefficient. What is its value and what is the interpretation of this number? (Choose the most appropriate answer. Note: numbers are truncated.)
b. -0.037; This is how much the selling price of the house will decrease in hundred thousand as the house age by a year.

10. Which of the two variables has better P-value and what is this P-value? (Note: numbers are truncated.)
c. #Bathroooms has the best P-value; P-value = 1.08E-09

11. Using this second table predict the selling price of a housethat is 10 years old, has 2 bathrooms and 3 rooms.
b. 12.57 hundred thousands
Explaination :
Regression equation
selling price = 0.98872665-0.0369(Age)+ 5.9745(#Bathrooms)
selling price = 0.98872665-0.0369(10)+ 5.9745(2) =12.5684

12. Based on the table would you characterize the Regression fit and the prediction as Poor, Good, Very Good, or Excellent?
c. Good
Fit of the regression line is determined by the coefficient of determination.

Coefficient of determination(rsqaure) = 0.805635082

It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 80.56%, hence the model is good