Question

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		$	4.14		$	73.98		4
2			4.08			54.90		2
3			5.76			138.86		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			7.17			77.58		7
14			5.94			146.51		6
15			6.60			162.69		8
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			6.71			59.83		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-2. Do you see any problem with multicollinearity?

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

The regression equation is:  

Food=_________+_________Income+________size.  

1. 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

Total

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 coefficients 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.)

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

5. State true or false.

From the graph the residuals appear normally distributed.

• True

• False

6. Choose the right option from the following graph.

• There is a homoscedasticity problem.

• There is no homoscedasticity problem.

Answer 1

using excel>data>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.888444702
R Square	0.789333989
Adjusted R Square	0.770182534
Standard Error	0.530246373
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	2	23.17631724	11.58815862	41.21535241	3.62693E-08
Residual	22	6.185546761	0.281161216
Total	24	29.361864
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.965917357	0.291805277	10.16402919	8.97101E-10	2.360750252	3.571084463
Income	0.002404743	0.002737645	0.878398687	0.389220407	-0.003272784	0.008082271
Size	0.484004724	0.056857249	8.512630051	2.07347E-08	0.366090007	0.601919441

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-2. Do you see any problem with multicollinearity?

No there is no multicollinierty

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

The regression equation is:  

Food=2.967+0.002*Income+0.484*size.  

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 $1 to the food bill.

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

R2 = 0.789

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.)

	df	SS	MS	F
Regression	2	23.1763	11.5882	41.22
Residual	22	6.1856	0.2812
Total	24	29.3619

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

H0 is rejected if F>3.44

c-4. Can we reject H0: = β1 = β2 = 0?

Reject H0. At least one of the regression coefficients is not equal to zero

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.)

	Coefficients	Standard Error	t Stat	P-value
Intercept	2.9659	0.2918	10.16	8.97101E-10
Income	0.0024	0.0027	0.89	0.389220407
Size	0.4840	0.0569	8.51	2.07347E-08

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

true.

From the graph the residuals appear normally distributed.

True

1. Choose the right option from the following graph.

• There is no homoscedasticity problem.