Question: [Problem 1:50 points] The excel file named, IME524_Quiz3.xlsxcontains a data set describing measurements of mean noise levels in dBA (y), roadway width (x1) and mean

[Problem 1:50 points] The excel file named, "IME524_Quiz3.xlsx"contains a data set describing measurements of mean noise levels in dBA (y), roadway width (x1) and mean speed (x2) at 10 city locations. This study was conducted by Pamanikabud and Tharasawatipipat in 1999. Answer the following questions. (a) Train a regression model of the form, y = Bo + B1X1 + B2X2 + B3X1X2 [10 points) (b) Compute the 95% confidence interval of the mean prediction at xy = 8 and xy = 33 [15 points) (e) Perform a hypothesis test using F-statistic to test if 3 = 0. Use a = 0.1 [10 points] (d) Use best subset regression method to identify the best model with two independent terms. Use R2 as a metric to identify the best model. [15 points] [Problem 1:50 points] The excel file named, "IME524_Quiz3.xlsx"contains a data set describing measurements of mean noise levels in dBA (y), roadway width (x1) and mean speed (x2) at 10 city locations. This study was conducted by Pamanikabud and Tharasawatipipat in 1999. Answer the following questions. (a) Train a regression model of the form, y = Bo + B1X1 + B2X2 + B3X1X2 [10 points) (b) Compute the 95% confidence interval of the mean prediction at xy = 8 and xy = 33 [15 points) (e) Perform a hypothesis test using F-statistic to test if 3 = 0. Use a = 0.1 [10 points] (d) Use best subset regression method to identify the best model with two independent terms. Use R2 as a metric to identify the best model. [15 points]

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