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Exercise 16.037 {Exercise 16.37} The following exercises require the use of a computer and software. Use...

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.

Homework Answers

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

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