Question

The appraisal of a warehouse can appear straightforward compared to other appraisal assignments. A warehouse appraisal involves comparing a building that is primarily an open shell to other such buildings. However, there are still a number of warehouse attributes that are plausibly related to appraised value. Consider the accompanying data on truss height (ft), which determines how high stored goods can be stacked, and sale price ($) per square foot.

Height	12	14	14	15	15	16	18	22	22	24
Price	35.55	37.82	36.92	40.02	38.02	37.50	40.98	48.51	46.98	47.52

Height	24	26	26	27	28	30	30	33	36
Price	46.20	50.36	49.15	48.07	50.89	54.78	54.30	57.17	57.44

(a)

Estimate the true average change in sale price associated with a one-foot increase in truss height, and do so in a way that conveys information about the precision of estimation. (Use a 95% CI. Round your answers to three decimal places.)

$  , $

(b)

Estimate the true average sale price for all warehouses having a truss height of 25 ft, and do so in a way that conveys information about the precision of estimation. (Use a 95% CI. Round your answers to three decimal places.)

  ,

dollars per square foot

(c)

Predict the sale price for a single warehouse whose truss height is 25 ft, and do so in a way that conveys information about the precision of prediction. (Use a 95% PI. Round your answers to three decimal places.)

  ,

dollars per square foot

How does this prediction compare to the estimate of (b)?

The prediction interval is  ---Select--- the same as smaller than wider than the confidence interval in part (b).

(d)

Without calculating any intervals, how would the width of a 95% prediction interval for sale price when truss height is 25 ft compare to the width of a 95% interval when height is 30 ft? Explain your reasoning.

Since 25 is  ---Select--- farther from nearer to the mean than 30, a PI at 30 would be  ---Select--- wider smaller than the PI at 25.

(e)

Calculate the sample correlation coefficient. (Round your answer to three decimal places.)

Interpret the sample correlation coefficient.

There is a  ---Select--- weak strong correlation between the variables.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

(a) (0.887, 1.085)

(b) (47.731, 49.173)

(c) (45.377, 51.527)

The prediction interval is wider than the confidence interval in part (b).

(d) Since 25 is farther from the mean than 30, a PI at 30 would be wider than the PI at 25.

(e) r = 0.981

There is a strong correlation between the variables.

	r²	0.963
	r	0.981
	Std. Error	1.417
	n	19
	k	1
	Dep. Var.	Price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	888.7680	1	888.7680	442.75	1.30E-13
Residual	34.1258	17	2.0074
Total	922.8938	18
Regression output				confidence interval
variables	coefficients	std. error	t (df=17)	p-value	95% lower	95% upper
Intercept	23.7953
Height	0.9863	0.0469	21.042	1.30E-13	0.887	1.085
Predicted values for: Price
		95% Confidence Interval	95% Prediction Interval
Height	Predicted	lower	upper	lower	upper	Leverage
25	48.45209	47.731	49.173	45.377	51.527	0.058

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