Question

Exercise 14-12 (LO14-7)

A real estate developer wishes to study the relationship between the size of home a client will purchase (in square feet) and other variables. Possible independent variables include the family income, family size, whether there is a senior adult parent living with the family (1 for yes, 0 for no), and the total years of education beyond high school for the husband and wife. The sample information is reported below.

Family		Square Feet		Income (000s)		Family Size		Senior Parent		Education
1		2,300		60.8		2		0		4
2		2,300		68.4		3		1		6
3		3,400		104.5		3		0		7
4		3,360		89.3		4		1		0
5		3,000		72.2		4		0		2
6		2,900		113		2		1		10
7		4,100		125.4		5		0		6
8		2,250		89.6		3		0		8
9		4,200		133		5		0		2
10		2,800		98		3		0		6

1. Develop an appropriate multiple regression equation using stepwise regression. (Use Excel data analysis and enter number of family members first, then their income and delete any insignificant variables. Leave no cells blank - be certain to enter "0" wherever required. R and R2 adj are in percent values. Round your answers to 3 decimal places.)

Step	1	2
Constant
Family Size
t-statistic
p-value
Income
t-statistic
p-value
S
R-Sq
R-Sq(adj)

2. Select all independent variables that should be in the final model. (You may select more than one answer. Single-click the box with the question mark to produce a check mark for a correct answer and double-click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)

• Senior parent
• Square feet
• Family size
• Income
• Education

Exercise 14-26 (LO14-1, LO14-2, LO14-4)

Many regions in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has motivated many of the large grocery store chains to build new stores in the region. The Kelley’s Super Grocery Stores Inc. chain is no exception. The director of planning for Kelley’s Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.

Family		Food			Income			Size
1		$	3.90		$	73.98		2
2			4.08			54.90		2
3			5.76			142.16		4
4			3.48			52.02		1
5			4.20			65.70		2
6			4.80			53.64		4
7			4.32			79.74		3
8			5.04			68.58		4
9			6.12			165.60		5
10			3.24			64.80		1
11			4.80			138.42		3
12			3.24			125.82		1
13			5.76			77.58		7
14			4.48			159.28		2
15			6.60			30.80		2
16			5.40			141.30		3
17			6.00			36.90		5
18			5.40			56.88		4
19			3.36			71.82		1
20			4.68			69.48		3
21			4.32			54.36		2
22			5.52			87.66		5
23			4.56			38.16		3
24			5.40			43.74		7
25			7.33			45.73		5

Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household.

1. a-1. Develop a correlation matrix. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

	Food	Income
Income
Size

a-2. Do you see any problem with multicollinearity?

1. There is

2. b-1. Determine the regression equation. (Round your answer to 3 decimal places.)

3. The regression equation is: Food=

   +

   Income +

   Size

4. b-2. How much does an additional family member add to the amount spent on food? (Round your answer to the nearest dollar amount.)

Another member of the family adds

to the food bill

1. c-1. What is the value of R²? (Round your answer to 3 decimal places.)

R2

1. c-2. Complete the ANOVA (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 4 decimal places and F to 2 decimal places.)

Source	DF	SS	MS	F	p-value
Regression
Error				BLANK	BLANK
Total			BLANK	BLANK	BLANK

1. c-3. State the decision rule for 0.05 significance level. H₀: = β₁ = β₂ = 0; H₁: Not all β_i's = 0. (Round your answer to 2 decimal places.)

H0 is rejected if F>

1. c-4. Can we reject H₀: = β₁ = β₂ = 0?

H0. At least one of the regression is

1. d-1. Complete the table given below. (Leave no cells blank - be certain to enter "0" wherever required. Round Coefficient, SE Coefficient, P to 4 decimal places and T to 2 decimal places.)

Predictor	Coefficient	SE Coefficient	t	p-value
Constant
Income
Size

1. d-2. Would you consider deleting either of the independent variables?

There is

to delete a variable

Answer 1

Exercise 14-12 (LO14-7)

a)

Model 1

Regression Equation

Square Feet = 1257.69 + 530.38 Family Size

Model 2

Regression Equation

Square Feet = 390.38 + 345.06 Family Size + 15.69 Income

b)

Final Model

Model 3

Hence, Only Income and Education should be in the final model.

Exercise 14-26 (LO14-1, LO14-2, LO14-4)

1)

A1)

A2)

There is no problem of multicollinearity

B1)

Regression Model

Regression Equation

Food = 3.42 + 0.0002 Income + 0.44 Size

B2)

An additional Member adds 0.44 units of food

C1)

R Square = 0.5231

C2)

	df	SS	MS	F	Significance F
Regression	2	14.23	7.11	12.07	0.00
Residual	22	12.97	0.59
Total	24	27.20

C3)

Reject H0. 

F Critical = 3.44

C4)

At least one of the coefficient is not zero

D1)

	Coefficients	Standard Error	t Stat	P-value
Intercept	3.42	0.46	7.42	0.00
Income	0.0002	0.00	0.06	0.95
Size	0.44	0.09	4.91	0.00

D2)

We should delete Income.