Question 546:

Asked on December 10, 2008

Tags: Regression Analysis , Slope , Regression Equation

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1. Q546_1_q546.xls

Regression equation is Total Revenue = 1.9254 + .0055(Total Assets)

The Null hypothesis is the slope is equal to 0. The alternative hypothesis is that the slope is NOT equal to 0. We'd reject Ho if the p-value is less than .05. The critical value of t for an alpha of .05 and 62 degrees of freedom can be found in your appendix, or using the excel function =TINV(.05,62) = 1.998. So we'd reject Ho if the t-value for the slope is greater than 1.998 

 Since the slope t-statistic of 8.183 is greater than the cutoff value of 1.998, we reject Ho and say the slope is significantly different than 0, and in this case positive.
The 95% confidence intervals around the slope suggest that a reasonable lower value of .034 and high-point of 13.30 are what we'd expect the slope to fluctuate between around 95% of the time if we were to take repeated samples. We see that it likely wont get much lower than .0452 but could get much larger.

The F-statistic can be used to test the significance of the slope, as well as other values. The t-statistic with d degrees of freedom can be squared to produce the F-statistic on 1 and d degrees of freedom. So the t of 8.183 with 62  degrees of freedom becomes an F of 69.66 with 1 and 62 degrees of freedom. Using the excel function =FDIST (69.66, 1, 62) we get p < .0001, the same as the p-value given in the output. See the attached sheet for the calculations.

The fit of this equation can be described by using the R2 statistic which is given as .519. We would say that total assets describes or explains around 51.9% of the variation in total revenue. This is a good fit and one predictor explains a lot of the variation.