The variables depression and anxiety are the self-reported depression and anxiet

Question

The variables depression and anxiety are the self-reported depression and anxiety, respectively, measured on the same day using a scale that can give values ranging between 0 (corresponds to min possible level) to 10 (max). Fit a regression model with Y = depression and X = anxiety and conduct an F-test of H_0: beta_1 = 0 vs. Ha: Beta_1 = 0. Give the formula for the test statistic (in symbols], the numerical value of the test statistic, the p value and a conclusion. When giving the numerical value of the test statistic, please make sure to show how the F statistic was calculated based on values given in the ANOVA table. Depression = 0.49 +0.71Anxiety t = x - mu_0/s T = 17.78 t^2 = F F = 316.21 = 680.5907/2.15 alpha = 0.05 P value is P(F(1, 198]> =316.21)

Explanation / Answer

If you measured in a 0-100 rather than 0-10, the slope of the regression will not change, but it will change the intercept term only. Hence, slope estimate of anxiety, if it were recorded on a 0-100 scale, is same with 0-10 scale that is

slope =0.71

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