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4. (18 points) A simple linear regression model is used to examine the relationship between the amount of time spent studying and the grade on an exam in a class with 18 students. The mean and standard deviation for the amount of time spent studying for the exam are 5 hours and 2 hours, respectively; the mean and standard deviation for the grade on the exam are 80 and 10, respectively. The correlation between the amount of time spent studying and the grade on the exam is 0.80. (1). Find the equation of the least-squares regression line for predicting the exam score of a student in the class based on the amount of time that the student spent studying. (2). Construct a 99% confidence interval for the slope b1 of the regression line of exam score on amount of studying. Round the endpoints to at least 3 decimal places. (Hint: The confidence interval is of the form b1 ± tSEb1 , where t is from t(n - 2) , SEb1 = s / sqrt(Sxx) and s^2 = SSE / (n - 2) = sum from i=1 to n of ei^2 / (n - 2) = sum from i=1 to n of (yi - y_hat i)^2 / (n - 2) = (n - 1)sy^2(1 - r^2) / (n - 2) .)

          4. (18 points) A simple linear regression model is used to examine the relationship between the amount of time spent studying and the grade on an exam in a class with 18 students. The mean and standard deviation for the amount of time spent studying for the exam are 5 hours and 2 hours, respectively; the mean and standard deviation for the grade on the exam are 80 and 10, respectively. The correlation between the amount of time spent studying and the grade on the exam is 0.80.

(1). Find the equation of the least-squares regression line for predicting the exam score of a student in the class based on the amount of time that the student spent studying.

(2). Construct a 99% confidence interval for the slope b1 of the regression line of exam score on amount of studying. Round the endpoints to at least 3 decimal places. (Hint: The confidence interval is of the form b1 ± t*SEb1 , where t* is from t(n - 2) , SEb1 = s / sqrt(Sxx) and s^2 = SSE / (n - 2) = sum from i=1 to n of ei^2 / (n - 2) = sum from i=1 to n of (yi - y_hat i)^2 / (n - 2) = (n - 1)sy^2(1 - r^2) / (n - 2) .)

4. (18 points) A simple linear regression model is used to examine the relationship between the amount of time spent studying and the grade on an exam in a class with 18 students. The mean and standard deviation for the amount of time spent studying for the exam are 5 hours and 2 hours, respectively; the mean and standard deviation for the grade on the exam are 80 and 10, respectively. The correlation between the amount of time spent studying and the grade on the exam is 0.80.

(1). Find the equation of the least-squares regression line for predicting the exam score of a student in the class based on the amount of time that the student spent studying.

(2). Construct a 99% confidence interval for the slope b1 of the regression line of exam score on amount of studying. Round the endpoints to at least 3 decimal places. (Hint: The confidence interval is of the form b1 ± t*SEb1 , where t* is from t(n - 2) , SEb1 = s / sqrt(Sxx) and s^2 = SSE / (n - 2) = sum from i=1 to n of ei^2 / (n - 2) = sum from i=1 to n of (yi - yhat i)^2 / (n - 2) = (n - 1)sy^2(1 - r^2) / (n - 2) .)

Added by Robert S.

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