Question

Exercise 16.037

{Exercise 16.37}

The following exercises require the use of a computer and software.
Use a 5% significance level for all tests of hypotheses.

Dataset:

Income	Food
53	188.24
47	304.89
59	304.99
44	283.99
87	316.21
56	263.32
62	315.87
60	201.52
70	295.5
85	318.53
63	278.78
57	254.34
59	253.79
64	310.97
45	215.79
62	248.34
63	299.66
55	220.72
77	319.58
52	280.96
72	259.73
64	254.5
68	181.99
54	256.8
63	258.54
57	203.91
67	280.53
47	244.72
58	231.56
58	251.03
58	268.9
57	290.88
66	255.45
67	282.11
63	313.17
62	315.62
49	290.75
42	179.35
70	295.35
42	212.32
69	306.64
28	198.63
53	297.26
59	274.37
44	224.85
61	278.45
54	268.98
67	302.73
55	253.92
56	299.79
74	255.84
33	205.05
67	321.05
55	261.07
50	209.31
52	259.45
47	209.45
48	205.54
59	323.6
60	278.02
50	238.45
46	219.23
70	339.11
56	214.62
53	242.81
72	274.19
70	290.19
35	290.62
58	297.82
71	258.05
53	262.68
77	305.65
68	301.15
61	286.05
77	372.7
58	359.45
57	279.15
63	224.78
52	292.83
58	253.61
64	278.5
55	230.16
62	209.75
41	237.57
45	201.13
55	202.3
58	255.45
70	225.63
41	285.83
81	328.84
52	286.69
56	212.78
76	324.03
65	272.59
67	272.98
67	281.9
45	212.01
82	322.49
65	262.41
49	292.43
75	352.52
49	286.22
59	279.15
63	292.5
59	298.82
58	303.49
69	279.99
62	225.89
76	257.84
55	219.79
58	230.49
64	250.28
42	251.44
60	309.87
61	226.83
70	180.32
55	301.32
38	192.63
60	337.91
78	312.57
59	360.24
64	223.94
59	269.02
53	303.28
53	254.32
55	276.84
53	204.96
49	265.98
58	254.62
63	309.24
46	262.44
74	324.89
60	306.96
70	327.97
41	218
48	249.08
59	289.11
53	294.35
60	290.44
44	287.45
65	277.71
58	267.21
76	311.81
60	271.93
69	385.03
65	220.19
72	304.07
80	330.5
59	257.37
81	313.64

An economist for the federal government is attempting to produce a better measure of poverty than is currently in use. To help acquire information, she recorded the annual household income (in $1,000s) and the amount of money spent on food during one week for a random sample of households.

a)  Determine the coefficient of determination (to 4 decimals) and describe what it tells you.
R² = ______

b) ______% of the variation in food budgets is explained by the variation in household income.

c)  Conduct a test to determine whether there is evidence of a linear relationship between household income and food budget.
There (Select one: is or is not) enough evidence to infer a linear relationship between food budget and household income.

Answer 1

Regression output using Excel

Regression Statistics
Multiple R	0.495853374
R Square	0.245870569
Adjusted R Square	0.2407751
Standard Error	36.93932351
Observations	150
ANOVA
	df	SS	MS	F	Significance F
Regression	1	65841.58033	65841.58	48.2528	1.1E-10
Residual	148	201948.016	1364.514
Total	149	267789.5963
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	153.8985946	17.01994055	9.042252	7.9E-16	120.2651	187.5321
Income	1.95820496	0.281901224	6.946422	1.1E-10	1.401134	2.515276

Therefore ,Answers

(a) R^2 = 0 .2459

( b ) 24 .59 %

( c ) is