Given are five observations for two variables, x and y. Use Table 2 of Appendix B. xi | 1 2 3 4 5 ---|---------- yi | 4 7 6 12 13 Round your answers to two decimal places. a. Using the following equation: Sy* = s * sqrt(1/n + (x* - x_bar)^2 / sum((xi - x_bar)^2)) Estimate the standard deviation of y_hat* when x = 3. b. Using the following expression: y_hat* +/- t_alpha/2 * s_y_hat* Develop a 95% confidence interval for the expected value of y when x = 3. c. Using the following equation: s_pred = s * sqrt(1 + 1/n + (x* - x_bar)^2 / sum((xi - x_bar)^2)) Estimate the standard deviation of an individual value of y when x = 3. d. Using the following expression: y_hat* +/- t_alpha/2 * s_pred Develop a 95% prediction interval for y when x = 3.
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Step 1: Calculate the standard deviation of € when I = 3 using the formula Sq(Ti). Show more…
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Given are five observations for two variables x and y. Use Table 2 of Appendix B. xi 1 2 3 4 5 yi 4 8 5 11 13 Round your answers to two decimal places. a. Using the following equation: Sy* = s * sqrt(1/n + (x* - x_bar)^2 / sum(xi - x_bar)^2) Estimate the standard deviation of y* when x = 3. b. Using the following expression: y* +/- t_alpha/2 * Sy* Develop a 95% confidence interval for the expected value of y when x = 3. c. Using the following equation: spred = s * sqrt(1 + 1/n + (x* - x_bar)^2 / sum(xi - x_bar)^2) Estimate the standard deviation of an individual value of y when x = 3. d. Using the following expression: y* +/- t_alpha/2 * spred Develop a 95% prediction interval for y when x = 3.
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