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# Univariate regression analysis

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It has been hypothesized that average thrust can be used as a basis for predicting the cost of rocket engines. It has been further hypothesized that average thrust and unit cost are positively correlated (i.e., unit cost increases as average thrust increases). You have been provided the following sample data set regarding the unit cost at unit 100 for twelve different rocket engine designs. (Note: Cost at unit 100 refers to the cost for the 100th unit in a production run. Focusing on the cost of a specific later unit in a large production run is often used as a means to more accurately compare steady-state production costs between different models of a product without the comparison being unduly influenced by the developmental costs for the different models that are typically incurred on the first few units produced.)

Rocket Engine Model Average Thrust (lbs) Cost (at unit 100)
1 877 \$9,753
2 4,907 \$7.11
3 1,394 \$12,354
4 2,645 \$97,228
5 13,145 \$56,721
6 14,345 \$45,987
7 26,290 \$911,234
8 43,323 \$999,000
9 31,298 \$937,510
10 37,500 \$1,454,350
11 88,000 \$1,481,090
12 86,135 \$1,721,800

Perform a univariate regression analysis using cost at unit 100 as the dependent variable and average thrust as the independent variable, with a 95% confidence level, in order to answer the following questions.

1) Does the regression model confirm a positive correlation between the dependent variable and the independent variable as hypothesized?

2) What is the desired statistical significance for the regression model?

3) Is the statistical significance of the model as a whole less than the desired statistical significance for the regression model?

4) Is the statistical significance of the linear relationship between the dependent and independent variable less than the desired statistical significance for the regression model?

5) Should the coefficient of determination or adjusted coefficient of determination be used to evaluate this regression model?

6) What percentage of the observed variation between the actual values of the dependent variable and the mean value of the dependent variable values in the sample data set is explained by the regression model?

7) What is the amount by which we will be off on average when predicting values for the dependent variable using the regression model?

8) What is the coefficient for the y-intercept for the regression model?

9) What is the coefficient for the independent variable for the regression model?

10) What is the estimated cost at unit 100 for a rocket engine with a design thrust of 45,000 pounds?