Question

Many regions along the coast 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. The director gathered the following sample information.

Family		Food		Income		Size
1		$3.84		$73.98		1
2		4.08		54.90		2
3		5.76		53.20		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		7.20		77.58		7
14		6.40		94.15		5
15		6.60		135.76		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		5.90		62.40		6

(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

(b-1)

Determine the regression equation. (Round your answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

The regression equation is: Food =  +  Income +  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 $  to the food bill.

(c-1)

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

(c-2)

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

Source	DF	SS	MS	F	p
Regression
Error
Total

(c-3)

Complete the ANOVA (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 3 decimal places and F to 2 decimal places.)

(d-1)

Complete the given below table. (Leave no cells blank - be certain to enter "0" wherever required. Do not round the intermediate calculations. Round T to 2 decimal places and all other values to 3 decimal places.)

Predictor	Coef	SE Coef	T	P
Income
Size

Answer 1

Correlation matrix is :

	Food	Income
Income	0.214	1
Size	0.911	0.127

(Using excal to find correlation we have command =correl(array1(select income column), array2 (select food column)))

Excel Output is :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.916257008
R Square	0.839526904
Adjusted R Square	0.824938441
Standard Error	0.460007547
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	2	24.35482325	12.17741162	57.54731596	1.81729E-09
Residual	22	4.655352752	0.211606943
Total	24	29.010176
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.961284867	0.267969205	11.05084022	1.90198E-10	2.40555075	3.51701898	2.40555075	3.517018984
Income	0.003093656	0.002679566	1.154536202	0.260667834	-0.002463424	0.00865074	-0.00246342	0.008650735
Size	0.483821397	0.046378329	10.43205762	5.56074E-10	0.38763863	0.58000416	0.38763863	0.580004164

Using Excel Output :

Part b-1. The regression equation is

Food = income + size

The general regression equation is ,

Y(food) = b0+b1*income + b2*size

Y (food) = 2.961+0.003*income+0.484*size    (rounded to 3 decimal )

Part b-2.

If family member is 1 (size = 1) then food cost will be $3.445

y = 2.961 + 0.484*1 = 2.961+0.484 = 3.445

If family member is 2 then food cost will be $3.929

y = 2.961+0.484*2 = 3.929

Ans : Means another family member adds $0.484 to the food bill . If no family member is add then food bill is $2.961.

Part . C-1 .

R2 = 0.839

Part C-2 .

Using F test we have F = 57.55

and P value = 0.00 and alpha = 0.05

P value (0.0000) < alpha (0.05) we reject H0 and conclude that Bi's is significant . (or we can say that model is significant).

Part C-3.

Rounded value into 2 decimal place.

ANOVA
	df	SS	MS	F	P
Regression	2	24.355	12.177	57.55	0.000
Error	22	4.655	0.212
Total	24	29.010

Part d-1.

Predictor	Coef	SE Coef	T	P
Income	0.003	0.003	1.15	0.261
Size	0.484	0.046	10.43	0.000

To get excel output . Enter data then select DATA ---> Data Analysis ----> Regression

y = select food column

x = select size and income column

Okay.