In the questions that follow, let Beta_1 be the coefficient for Vmag, or the slope parameter. (a) What is my test statistic for the following hypothesis test: H_0: Beta_1 = 0; H_a: Beta 1 is not equal to 0? [ Select] (b) What is our estimated value for Beta 1? [Select] (c) What is the 95% confidence interval for Beta 1? [Select] (d) True or False: We would reject the null hypothesis at an alpha 0.05 level for the hypothesis test in part (a). [Select] (e) If I have a star with a Vmag of 16 and a B-V of 2, what would its residual be? [ Select] (f) What is the predicted value for a star with a Vmag of 9? Select ] (g) What is the true linear model for all stars astronomers study? [Select] (h) What is the value of r, the correlation coefficient, for this analysis? [ Select] As a budding astronomer, you are interested in the information you can glean from just measuring how bright a star is. You randomly sample 137 stars studied by astronomers and obtain the visual band magnitude (Vmag, how bright the star appears to us on earth) along with a measure of the magnitude (or size) of the star, called "B-V" in the dataset. Specifically, you are interested if the Vmag can help you predict the magnitude of the star. You fit a linear model and obtain the following output: Call: Im(formula = 'B-V Vmag, data mod_dat) Residuals: 10 -0.79879 -.11223 -0.04728 Min Median 3Q 0.07450 Max 0.96407 Coefficients: Estimate Std. Error t value Pr(>Itl) (Intercept) -0.330997 Vmag 0.078718 -4.205 4.73e-05 *** 0.134130 0.009287 14.443 < 2e-16 *** Signif. codes: 0 **** 0.001 ** 0.01 ** 0.05 '.' 0.1 1 Residual standard error: 0.2023 on 135 degrees of freedom Multiple R-squared: 0.6071, F-statistic: 208.6 on 1 and 135 DF, p-value: < 2.2e-16 Adjusted R-squared: 0.6042