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You have 82 observations with which to estimate a regression model of the form yi = ˆα+βxˆi. Supposefurther that the sum of squared residuals P82i=1 2i = 2156.36.
(a) What is the standard deviation of the regression?
(b) Suppose ˆα = .78 and βˆ = 1.75. What is your prediction for yi when xiis 10? Is it likely that yourprediction will be true? Why or why not?
(c) Suppose the sum of squared deviations from the mean of x, P82i=1(xi - x¯)2 = 47.57. What is thestandard error for βˆ?
(d) Test the two-sided hypothesis where HO : β = 0 and HA : β 6= 0. Remember to use the estimatefor βˆ in the numerator and your answer for part (c) in the denominator to construct a t - stat,then compare it to some relevant critical value, at whatever level you want.
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