Question 3 (5+10+5+5+10+5+10+5-55p-) A random sample of data for 6 subjects produced the following data values (y is dependent and x is independent). You are conducting simple linear regression analysis. Calculate SST (Total sum of squares). Compute and interpret h. Compute and interpret b. Write the estimated regression equation. Calculate SSR (Regression sum of squares) and SSE (Error sum of squares). Compute the coefficient of determination and interpret it. Test the hypothesis Hu: B0 versus H: R with α = 0.05. Find the simple correlation coefficient value between x and y.
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Calculate SST (Total sum of squares) First, we need to find the mean of y values, denoted as $\bar{y}$. Then, we can calculate SST as follows: $$SST = \sum_{i=1}^{n}(y_i - \bar{y})^2$$ Show more…
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A random sample of data for 6 subjects produced the following data values (y is dependent and x is independent). You are conducting simple linear regression analysis. y x 47 5 38 7 32 11 24 12 22 19 10 25 i) Calculate SST (Total sum of squares). ii) Compute and interpret b1. iii) Compute and interpret b0. iv) Write the estimated regression equation. v) Calculate SSR (Regression sum of squares) and SSE (Error sum of squares). vi) Compute the coefficient of determination and interpret it. vii) Test the hypothesis H0 : ̂β1 = 0 versus H1 : ̂β1 ≠ 0 with α = 0,05 . viii) Find the simple correlation coefficient value between x and y.
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For questions A-D, based on the equation below, the regression of Y on X is "0.30", and the value of “X” is 10. Y = 5 + 0.3X A) What is the predicted value of "Y" when X is 10? ANSWER:_______________ B) If the observed value of Y is ten, what is the contribution of this XY pair to the residual sum of squares for the sample that contains this pair of values? ANSWER:_____________________________ C) If the mean of all the X values in the sample is six, what is the contribution of this X,Y pair to the sum of squares for the regression effect? ANSWER:___________________________ D) If the mean of all the X values for this X,Y pair is six, and the mean of the Y values is five, what is the contribution of this pair of X,Y values to the sum of the products (also called "cross products)? ANSWER:____________________________
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