##### Question

In: Statistics and Probability

# People in the aerospace industry believe the cost of a space project is a function of...

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 se.

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, SSxx = 89.333 and Se = 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)

## Solutions

##### Expert Solution

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 21.078

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)

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