Consider the following regression output, from relating the amount of time people spend watching TV in...

 

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Consider the following regression output, from relating the amount of time people spend watching TV in a day and their cholesterol levels. regress cholesterol time_tv Source Model Residual Total cholesterol time_tv _cons SS 5.04902329 28.3220135 33.3710367 df .0440691 -2.134777 1 5.04902329 .289000137 Coef. Std. Err. MS .337081179 .0105434 1.813099 t P>|t| 4.18 0.000 -1.18 0.242 Number of obs = F(1, Prob> F = R-squared Adj R-squared Root MSE = 100 17.47 0.0001 0.1426 -.53759 [95% Conf. Interval] a) Draw graphically and very precisely this relationship. (use grids) (2 marks) b) Calculate the R-squared, show and explain the steps. (it's approximately 0.15, but I don't really care about the final answer, I want to know how you get there). (2 marks) c) Calculate the degrees of freedom in the model that your F-statistic uses. (it's 98, but what I care about is how you get there). (2 marks) d) Calculate both estimated coefficients' 95% confidence intervals. (it's approximately {0.023;0.064} for time_tv and {-5.73;1.46} for the constant, but what I care about is how you get there). What is the statistical principle that allows you to calculate these 95% confidence intervals, just by looking at outputs in this table above? (3 marks) e) What is the F-test's null hypothesis that is clearly being rejected here? (Given that the F-value is above the critical value for rejection of the null). (3 marks) What is the unbiased estimator of population residuals' variance? Can you tell how much it is, just by looking at this table? (2 marks) f) Consider the following regression output, from relating the amount of time people spend watching TV in a day and their cholesterol levels. regress cholesterol time_tv Source Model Residual Total cholesterol time_tv _cons SS 5.04902329 28.3220135 33.3710367 df .0440691 -2.134777 1 5.04902329 .289000137 Coef. Std. Err. MS .337081179 .0105434 1.813099 t P>|t| 4.18 0.000 -1.18 0.242 Number of obs = F(1, Prob> F = R-squared Adj R-squared Root MSE = 100 17.47 0.0001 0.1426 -.53759 [95% Conf. Interval] a) Draw graphically and very precisely this relationship. (use grids) (2 marks) b) Calculate the R-squared, show and explain the steps. (it's approximately 0.15, but I don't really care about the final answer, I want to know how you get there). (2 marks) c) Calculate the degrees of freedom in the model that your F-statistic uses. (it's 98, but what I care about is how you get there). (2 marks) d) Calculate both estimated coefficients' 95% confidence intervals. (it's approximately {0.023;0.064} for time_tv and {-5.73;1.46} for the constant, but what I care about is how you get there). What is the statistical principle that allows you to calculate these 95% confidence intervals, just by looking at outputs in this table above? (3 marks) e) What is the F-test's null hypothesis that is clearly being rejected here? (Given that the F-value is above the critical value for rejection of the null). (3 marks) What is the unbiased estimator of population residuals' variance? Can you tell how much it is, just by looking at this table? (2 marks) f)