Question

People in the aerospace industry believe the cost of a space project is a function of the mass of the major object being sent into space. Use the following data to develop a regression model to predict the cost of a space project by the mass of the space object. Determine r² and s_e.

Weight (tons)	Cost ($ millions)
1.897	$ 53.6
3.019	184.9
0.453	6.4
0.971	23.5
1.058	33.1
2.100	110.4
2.385	104.6

*(Do not round the intermediate values. Round your answers to 4 decimal places.)
**(Round the intermediate values to 4 decimal places. Round your answer to 3 decimal places.)

2) For a least squares regression line, the sum of the residuals is __________.

a) sometimes positive and sometimes negative

b) always zero

c) always positive

d) always negative

3) In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, SS_xx = 89.333 and S_e = 3.44. A 95% confidence interval for the average of y when x = 8 is _________.

a) (3.56, 22.62)

b) (10.31, 15.86)

c) (9.13, 17.05)

d) (12.09, 14.09)

Answer 1

using excel>data >data analysis >regression

we have

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.9521
R Square	0.9065
Adjusted R Square	0.8878
Standard Error	21.0780
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	21547.3807	21547.3807	48.4994	0.0009
Residual	5	2221.4078	444.2816
Total	6	23768.7886
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-38.7124	18.0116	-2.1493	0.0843	-85.0126	7.5878
Weight (tons)	66.2700	9.5159	6.9641	0.0009	41.8087	90.7314

Ans 1 )

R Square

0.9065

Standard Error

21.0780

2) For a least squares regression line, the sum of the residuals is b) always zero

3) In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, SSxx = 89.333 and Se = 3.44. A 95% confidence interval for the average of y when x = 8 is 13.08+/- 2.78*3.44 = (3.56, 22.62)

option a is true

a) (3.56, 22.62)