# T-test for slope in the regression analysis

I would be grateful to any experts in regressions for a step-by-step explanation of some simple regression estimations - please see the two attached files.

Attached to this post is an Excel spreadsheet which contains two time series, X and Y.

To fully understand how the B0 and B1 estimators are estimated, I would be grateful for a step-by-step explanation of their computation in Excel, in the following equation:

Yt = B0 + B1Xt + ut, t = 1988q1, 1988q2, ......, 2007q4,

as well as an interpretation of the two estimates.

It would also be helpful if you could obtain the series of residuals, and show step by step how to obtain the standard error and the R-squared statistic for the regression, as well as the standard errors of the estimators of B1 and B0.

To understand the t tests and the F tests, I would be grateful for a step-by-step explanation of how to:

- perform a t test of the null hypothesis, Ho: B1 = 0, against the alternative hypothesis, Ha: B1 ≠ 0, and

- Perform a t test of the null hypothesis, Ho: B0 = 0, against the alternative hypothesis, Ha: B0 ≠ 0.

Finally, an explanation of how to compute the value of the F statistic for the significance of the regression, and of the relationship between the value of the F statistic and the value of the t statistic which was computed in relation to the null hypothesis, Ho: B1 = 0.

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#### Solution Summary

The solution gived detailed steps on conducting the t-test for slope in the regression analysis. All formula and calculations are shown and explained.