L

If we make the additional assumption that the intercept and slope estimates are normally distributed, the parameter estimate and the standard error can be combined to get a "t statistic" that measures whether the relationship is statistically significant.

T statistic for intercept = a/SEa T statistic from slope = b/SEb

For samples with more than 120 observations, a t statistic greater than 1.66 indicates that the variable is significantly different from zero with 95% certainty, while a statistic greater than 2.36 indicates the same with 99% certainty. For smaller samples, the t statistic has to be larger to have statistical significance.20

20 The actual values that t statistics need to take on can be found in a table for the t distribution, which is reproduced at the end of this book as an appendix.

The regression that measures the relationship between two variables becomes a multiple regression when it is extended to include more than one independent variables (X1,X2,X3,X4..) in trying to explain the dependent variable Y. While the graphical presentation becomes more difficult, the multiple regression yields a form that is an extension of the simple regression.

The R-squared still measures the strength of the relationship, but an additional R-squared statistic called the adjusted R squared is computed to counter the bias that will induce the R-squared to keep increasing as more independent variables are added to the regression. If there are k independent variables in the regression, the adjusted R squared is computed as follows -

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