Question

Thailand, Vietnam, and China have had a fast population increase over the last 10 years. It is expected that the growth will continue over the next 10 years. Therefore, many food companies that want to build new restaurants in these countries. McDonald's is no exception. The director of planning for McDonald's wants to study adding more restaurants in these countries. He believes there are two main factors that indicate the amount families spend on Food. 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			Family 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.

  Click here for the Excel Data File

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

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

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

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.)

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

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.)

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.)

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

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

Thailand, Vietnam, and China have had a fast population increase over the last 10 years. It is expected that the growth will continue over the next 10 years. Therefore, many food companies that want to build new restaurants in these countries. McDonald's is no exception. The director of planning for McDonald's wants to study adding more restaurants in these countries. He believes there are two main factors that indicate the amount families spend on Food. 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	Family 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.

  Click here for the Excel Data File

1. a-1. Develop a correlation matrix.

the correlation matrix is

	Food	Income	Family Size
Food	1
Income	-0.021	1
Family Size	0.723	-0.041	1

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

NO

using excel>data>data analysis >regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.723284
R Square	0.523139
Adjusted R Square	0.479788
Standard Error	0.767853
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	2	14.22999	7.114993	12.06754	0.00029
Residual	22	12.97115	0.589598
Total	24	27.20114
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3.416912	0.460734	7.416242	2.03E-07	2.461409	4.372415
Income	0.000241	0.003871	0.062135	0.951017	-0.00779	0.008269
Family Size	0.443042	0.090218	4.910765	6.54E-05	0.25594	0.630143

b-1. Determine the regression equation.

the regression equation is

Food = 3.417 +0.000 *Income +0.443*Family size

b-2. $0.443$ an additional family member add to the amount spent on food

c-1. the value of R2 is 0.523

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	14.2300	7.1150	12.07
Residual	22	12.9712	0.5896
Total	24	27.2011

c-3. State the decision rule for 0.05 significance level. H0: = β1 = β2 = 0; H1: Not all βi's = 0.

Reject Ho if F > 3.44

c-4. Can we reject H0: = β1 = β2 = 0

yes

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	3.4169	0.4607	7.41	0.0000
Income	0.0002	0.0039	0.0621	0.9510
Family Size	0.4430	0.0902	4.9108	0.0000

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

yes , the income variable should be deleted

* graph not given