Question

1.

Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 + 5.31 x3 predicts an adult’s height (y) given the individual’s mother’s height (x1), his or her father’s height (x2), and whether the individual is male (x3 = 1) or female (x3 = 0). All heights are measured in inches. In this equation, the coefficient of ______ means that ______.

x2; if two individuals have fathers whose heights differ by 1 inch, then the individuals’ heights will differ by 0.41 inches.

x2; if two individuals have mothers whose heights differ by 1 inch, then the individuals’ heights will differ by 0.41 inches.

x1; if two individuals have mothers whose heights differ by 0.5 inch, then the individuals’ heights will differ by 0.32 inch.

x3; a brother is expected to be 5.31 inches taller than his sister

x1; if two individuals have mothers whose heights differ by 0.32 inch, then the individuals’ heights will differ by 1 inch.

2.The following is a partial computer output of a multiple regression analysis of a data set containing 20 sets of observations on the dependent variable

The regression equation is
SALEPRIC = 1470 + 0.814 LANDVAL + 0.820 IMPROVAL + 13.5 AREA

Predictor	Coef	SE Coef	T	P
Constant	1470	5746	0.26	0.801
LANDVAL	0.8145	0.5122	1.59	0.131
IMPROVAL	0.8204	0.2112	3.88	0.0001
AREA	13.529	6.586	2.05	0.057

S = 79190.48

R-Sq = 89.7%

R-Sq(adj) = 87.8%

Analysis of Variance

Source	DF	SS	MS
Regression	3	8779676741	2926558914
Residual Error	16	1003491259	62718204
Total	19	9783168000

For the problem above, we want to carry out the significance test about the coefficient of LANDVAL, what is the t-value for this test, and is it significant?

46.66, significant

1.59, not significant

2.05, significant

0.26, not significant

3.

A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x₁ – 2.5 x₂, to predict y = the market price of a home (in $1,000s), using independent variables, x₁ = the total number of square feet of living space, and x₂ = the age of the house in years. The regression coefficient of x₁ suggests this: __________.

The addition of 1 square foot area of living space results in a predicted increase of $0.068 in the price of the home if the age of the home were held constant

The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the home if the age of the home were held constant

The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the home with the age of the home allowed to vary

The addition of 1 square foot area of living space results in a predicted increase of $0.068 in the price of the home for homes of different ages

4.The test statistic used to test the overall significance of a multiple regression model, the null hypothesis that each one the β-coefficients of the x-variables in the model is equal to zero, is tested against the alternative hypothesis that at least one the β-coefficients of the x-variables in the model is ≠ zero, is the __________.

χ² statistic

F value from the F-distribution tables

t statistic

F value calculated as mean square regression divided by mean square error

5.When additional independent variables are added to a simple linear regression, the coefficient of determination, R² may __________.

become negative

increase or stay the same

stay the same

decrease or stay the same

Answer 1

Sol:

1).

. x3; a brother is expected to be 5.31 inches taller than his sister.

2).

Option 1.59 and not significant

From the output provided

LANDVAL Coefficient = 0.8145

T value = 1.59

p value = 0.131

Since p value > 0.05 it is not significant

(commonly used p value is of 0.05

3).

0.068 * 1000 = $68

The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the home if the age of the home were held constant.

4).

The null hypothesis H₀ : each one theβ-coefficients of the x-variables in the model is equal to zero

against alternative hypothesis H₁ : at least one theβ-coefficients of the x-variables in the model is ≠ zero

The test statistic used to test the overall significance of a multiple regression model -

ans-> F value calculated as mean square regression divided by mean square error.

5).

When additional independent variables are added to a simple linear regression, the coefficient of determination, R2 may increase due to R-squared higher because it has more predictors

Therefore ,

increase of stay the same

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