Given that the fitted regression is Y = 76.40 - 6.388X₁ + 0.870X₂, the standard error of b₁ is 1.453, and n = 63, at α = .05, we can conclude that X₁ is a significant predictor of Y.

Question

Quizplus · Accepted Answer

Since the standard error of b₁ is given and n is large enough (n=63), we can use the t-distribution to perform a hypothesis test on the coefficient of X₁. Given α=.05, we can find the t-critical value for a two-tailed test with 61 degrees of freedom to be approximately 2.000. Using this value, we can calculate the t-statistic as (-6.388-0)/1.453 = -4.392. This t-statistic falls outside the range of -2.000 to 2.000, meaning that the coefficient is significant and we reject the null hypothesis that the coefficient is equal to 0. Therefore, we can conclude that X₁ is a significant predictor of Y.

Given That the Fitted Regression Is Y = 76