A real estate builder wishes to determine how house size (House) is influenced b
ID: 3127459 • Letter: A
Question
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. The output is provided below:
Variable
Coefficient
t-statistic
Constant
-1.633
-0.281
Income
0.448
3.954
Size
4.216
5.286
School
-0.6517
-1.509
R2 =0.75; Adjusted R2 = 0.73
F = 6.43
i. Referring to above, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
II. Referring to above, what are the degrees of freedom for this F-statistic?
A) 46 for the numerator, 4 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator
IIi. Referring to above, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
A) 0.00005
B) 0.001
C) 0.01
D) 0.05
IV. Referring to above, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000, having a family size of four, and going to school a total of 13 years?
A) 11.43
B) 15.15
C) 24.68
D) 53.87
V. Referring to above one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point?
A) 7.40
B) 2.52
C) – 2.52
D) – 4.89
Variable
Coefficient
t-statistic
Constant
-1.633
-0.281
Income
0.448
3.954
Size
4.216
5.286
School
-0.6517
-1.509
R2 =0.75; Adjusted R2 = 0.73
F = 6.43
Explanation / Answer
i. Referring to above, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
There are n=50 families and k=3 independent variables. The degree of freedom for error = n-k-1=50-3-1=46
By using excel finction =TDIST(test statistic, df, 2), the p-values are:
Two p-values are less than 0.01. Therefore, correct option is:
A) 0.01
II. Referring to above, what are the degrees of freedom for this F-statistic?
There are n=50 families and k=3 independent variables.
The numerator degree of freedom = k = 3
The denominator degree of freedom = n-k-1 = 50-3-1 = 46
Therefore, correct option is:
D) 3 for the numerator, 46 for the denominator
IIi. Referring to above, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
By using excel function =FDIST(6.43,3,46), the p-value = 0.00099
The smallest level of significance for which the regression model as a whole is significant (p-value is less than that value) is 0.001. Therefore, correct option is:
B) 0.001
IV. Referring to above, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000 = 40 thousand, having a family size of four, and going to school a total of 13 years?
The regression equation is:
House size = -1.633 + 0.448 Income in thousand + 4.216 Size - 0.6517 School
= -1.633 + 0.448(40) + 4.216(4) - 0.6517(13) = 24.6789
Therefore, correct option is:
C) 24.68
V. Referring to above one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point?
The regression equation is:
House size = -1.633 + 0.448 Income in thousand + 4.216 Size - 0.6517 School
= -1.633 + 0.448(100) + 4.216(10) - 0.6517(16) = 74.8998
Actual value = 7000 = 70 hundreds of square feet
Residual = Actual - Predicted = 70 - 74.8998 = -4.8998
Therefore, correct option is:
D) – 4.89
Test statistic Excel formula p-value 3.954 =TDIST(-1.633, 46, 2) 0.0003 5.286 =TDIST(5.286, 46, 2) 0.0001 -1.509 =TDIST(-1.509, 46, 2) 0.1383Related Questions
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