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		$	4.07		$	73.98		3
2			4.08			54.90		2
3			5.76			121.19		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			6.93			77.58		7
14			5.05			173.34		6
15			6.60			158.57		5
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			7.67			36.74		4

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.

rev: 02_27_2018_QC_CS-119840

Answer 1

a-1.

	Food	Income
Income	.151
Size	.779	.188

a-2. There is no problem with multicollinearity.

b-1. Food = 3.157 + 0.000*Income + 0.510*Size

b-2. 1

c-1. 0.608

c-2.

Source	SS	df	MS	F
Regression	19.3277	2	9.6638	17.03
Residual	12.4831	22	0.5674
Total	31.8107	24

c-3. 3.44

c-4. Reject, different from 0

d-1.

variables	coefficients	std. error	t (df=22)	p-value
Intercept	3.1568	0.4248	7.43	0.0000
Income	0.0001	0.0037	0.04	0.9723
Size	0.5096	0.0890	5.73	0.0000

d-2. Yes

False

There is a homoscedasticity problem.