Question

People in the aerospace industry believe the cost of a space project is a function of the weight of the major object being sent into space. You will use the following data to develop a regression model to predict the cost of a space project by the weight of the space object. Object Weight (tons) 1.897 Project Cost ($millions) 53.6 184.9 3.019 0.453 6.4 0.988 1.058 2.100 2.387 11.902 23.5 33.4 110.4 7 104.6 Totals: 516.8

A.) Construct an appropriate interval estimate of the mean cost of all space projects when the weight of the major object being sent into space is 1.5 tons, with 95% confidence. Interpret the practical meaning of this interval estimate, in plain English.

B.) Construct an appropriate interval estimate of the cost of a single space project when the weight of the object being sent into space is 1.5 tons, with 95% confidence. Interpret the practical meaning of this interval estimate, in plain English.

C.) Construct a 95% confidence interval estimate of the true population slope for this least squares regression line. Interpret the practical meaning of your interval estimate, in plain English.

Answer 1

Result:

A.) Construct an appropriate interval estimate of the mean cost of all space projects when the weight of the major object being sent into space is 1.5 tons, with 95% confidence. Interpret the practical meaning of this interval estimate, in plain English.

95% CI = (39.426, 81.648)

We are 95% confident that the mean cost of all space projects when the weight of the major object being sent into space is 1.5 tons falls in the interval (39.426, 81.648).

B.) Construct an appropriate interval estimate of the cost of a single space project when the weight of the object being sent into space is 1.5 tons, with 95% confidence. Interpret the practical meaning of this interval estimate, in plain English.

95% PI = (2.263, 118.812)

We are 95% confident that the mean cost of a single space project when the weight of the major object being sent into space is 1.5 tons falls in the interval (2.263, 118.812).

C.) Construct a 95% confidence interval estimate of the true population slope for this least squares regression line. Interpret the practical meaning of your interval estimate, in plain English.

95% CI for the true population slope = (41.787, 90.939).

We are 95% confident that   the true population slope falls in the interval (41.787, 90.939).

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	r²	0.906	n	7
	r	0.952	k	1
	Std. Error of Estimate	21.130	Dep. Var.	cost
Regression output						confidence interval
variables		coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	a =	-39.007	18.111	-2.154	.0838	-85.564	7.550
weight	b =	66.363	9.560	6.941	.0010	41.787	90.939
ANOVA table
Source	SS	df	MS	F	p-value
Regression	21,512.104	1	21,512.104	48.18	.0010
Residual	2,232.350	5	446.470
Total	23,744.454	6
Predicted values for: cost
		95% Confidence Interval		95% Prediction Interval
weight	Predicted	lower	upper	lower	upper	Leverage
1.5	60.537	39.426	81.648	2.263	118.812	0.151