Age Weight (pounds) 56 156 35 110 22 80 57 91 40 90 22 150 48...

Age	Weight (pounds)
56	156
35	110
22	80
57	91
40	90
22	150
48	165
48	99
25	189
40	178
25	123
25	190
59	255
49	112
33	155
56	134
20	117
31	91
27	100
23	80
45	190
29	255
31	112
59	200
39	134
35	110
44	99
27	110
24	180
27	150

The data represents the age and weight (in pounds) of 30 Langley residents. Create a model to predict the expected weight of an individual based on their age. Maintain a minimum of 4 decimal places for intermediate calculations.

a) What is the expected weight of an individual that is 27 years old?

b) How much variability in weight is accounted for by an individual’s age?

c) How much variability in weight is accounted for by factors other than age?

d) Assume alpha is 0.05 Is an individual’s weight a significant predictor of an individual’s age? Provide the specific statistical evidence from your Excel output to support your answer.

Expert Solution

(a) The model is:

Weight = 113.9148 + 0.7153*Age

The expected weight of an individual that is 27 years old is 133.228.

(b) 0.035

(c) 0.965

(d) The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.3189.

Since the p-value (0.3189) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that an individual’s weight is a significant predictor of an individual’s age.

	r²	0.035
	r	0.188
	Std. Error	47.834
	n	30
	k	1
	Dep. Var.	Weight (pounds)

ANOVA table
Source	SS	df	MS	F	p-value
Regression	2,355.8722	1	2,355.8722	1.03	.3189
Residual	64,066.2945	28	2,288.0819
Total	66,422.1667	29


Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	113.9148
Age	0.7153	0.7049	1.015	.3189	-0.7287	2.1593

Predicted values for: Weight (pounds)
		95% Confidence Interval	95% Prediction Interval
Age	Predicted	lower	upper	lower	upper	Leverage
27	133.228	110.508	155.949	32.645	233.811	0.054

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orchestra answered 2 years ago

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