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

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

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

The regression equation is: Food = ____ + _____ income + _____ size

3. 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.

4. What is the value of R²?

5. 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

6. State the decision rule for 0.05 significance level. H₀: = β₁ = β₂ = 0; H₁: Not all β_i's = 0.

7. 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

Answer 1

Here I attach the R code used along with the corresponding output.

d=read.csv("C:\\Users\\admin\\Desktop\\d.csv")
d
round(cor(d),3)
f=lm(d$food~d$income+d$Size)
summary(f)

anova(f)

(1)

(2) The obtained model is: food=2.966+0.002*income+0.484*size

(3) near 4 dollars an additional family member add to the amount spent on food

(4)

R square value is 0.789.

(5)

(6) All variables are significant.

(7)