Thirty data points on Y and X are employed to estimate the parameters in the lin

Question

Thirty data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is Dependent Variable: Y R-Square F-Ratio P-Value on F Observations: 30 0.3301 13.79 0.0009 Variable Parameter Standard T-Ratio P-Value Estimate Error Intercept 93.54 46.21 2.02 0.0526 X -3.25 0.875 -3.71 0.0009 a. The equation of the sample regression line is Y = _________________. b. There are ______ degrees of freedom for the t-test. At the 1% level of significance, the critical t-value for the test is ______________. c. At the 1% level of significance, a __________ (is, is not) significant, and b ________ (is, is not) significant. d. At the 2% level of significance, the critical t-value for a t-test is ___________. At the 2% level of significance, a ____________ (is, is not) significant, and b ____________ (is, is not) significant. e. The p-value for b indicates that the exact level of significance is ______ percent, which is the probability of _________________________________ _____________________________________________________________. f. At the 1% level of significance, the critical value of the F-statistic is __________. The model as a whole ______________(is, is not) significant at the 1% level. g. If X equals 500, the fitted (or predicted) value of Y is __________________. h. The percentage of the total variation in Y not explained by the regression is ______________ percent. i. Explain why it is necessary to assess the statistical significance of the parameter estimates.

Explanation / Answer

a. The equation of the sample regression line is: = _____ y = 76.25 - 124.20*X _____. b. There are __30____ degrees of freedom for the t-test. At the 5% level of significance, the critical t-value for the test is ______2.042________. c. At the 5% level of significance, ____Intercept is ______ (is, not) significant, and ___Slope is_____ (is, is not) significant. d. At the 2% level of significance, the critical t-value for a t-test is _____2.457______. At the 2% level of significance, ___Intercept is not______ (is, is not) significant, and ____Slope is_____ (is, is not) significant. e. The p-value for indicates that the exact level of significance is __1.24____ percent, which is the probability of ________Slope being zero__________. f. At the 5% level of significance, the critical value of the F-statistic is __4.171_____. The model as a whole ___is________(is, is not) significant at the 5% level. g. If X equals 240, the fitted (or predicted) value of Y is ___________-29731.75_________________. h. The percentage of the total variation in Y that is NOT explained by the regression is ___80.89_____.

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