In-Class Assignment 15a- Question 3

2/14/24, 12:17 AM In-Class Assignment 15a-Diatra Serra https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/7 Student: Diatra Serra Date: 02/14/24 Instructor: Victor Law Course: 202410 BUSN 3431 050 Assignment: In-Class Assignment 15a Consider the following set of dependent and independent variables. Complete parts a through e below. y 10 13 13 16 18 25 26 33 x 1 3 2 3 7 9 9 19 17 x 2 14 12 11 12 2 10 5 3 Click here to view a partial table of critical F-scores for a significance level of 0.05. 1 a) Use technology to identify the SST, SSR, and SSE. Use technology to preform a multiple regression for the given data and identify the values for the SST, SSR, and SSE in the resulting ANOVA table. The value of the total sum of squares, SST, is , rounded to two decimal places. 443.50 The value of the sum of squares regression, SSR, is , rounded to two decimal places. 357.98 The value of the sum of squares error, SSE, is , rounded to two decimal places. 85.52 b) Calculate the multiple coefficient of determination. The multiple coefficient of determination is given by the following formula, where SSR is the sum of squares regression and SST is the total sum of squares. R 2 = SSR SST Substitute the values SSR and SST into the formula and evaluate, rounding to three decimal places. = 357.98 = 443.50 R 2 = SSR SST R 2 = 357.98 443.50 R 2 = 0.807 c) Test the significance of the overall regression model using . = 0.05 The null hypothesis assumes no relationship exists between the dependent and independent variables, whereas the alternative hypothesis takes the opposite position. Note that 1 is the coefficient of x 1 and 2 is the coefficient of x 2 in the regression model. The null and alternative hypotheses are shown below. H 0 : 1 2 0 (No relationship between the variables) = = H 1 : At least one i 0 (Relationship exists between the variables) ≠

2/14/24, 12:17 AM In-Class Assignment 15a-Diatra Serra https://tdx.acs.pearsonprd.tech/api/v1/print/highered 2/7 Identify the value of the F-test statistic. The formula for the F-test statistic is given below, where MSR is the mean square regression and MSE is the mean square error. F = MSR MSE First calculate the MSR and MSE. The formula for the MSR is given below, where k is the number of independent variables. MSR = SSR k The independent variables are the x-variables. Use the data table to identify the number of independent variables. k = 2 Substitute the values SSR and k into the formula and evaluate. = 357.98 = 2 MSR = SSR k MSR = 357.98 2 MSR = 178.990 The formula for the MSE is given below, where n is the sample size. MSE = SSE n − k − 1 The sample size is the number of observations. Use the data table to identify the sample size. n = 8 Substitute the values SSE , n , and k into the formula and evaluate. = 85.52 = 8 = 2 MSE = SSE n − k − 1 MSE = 85.52 5 MSE = 17.104 Now calculate the F-test statistic. Substitute the values MSR and MSE into the formula and evaluate, rounding to two decimal places. = 178.990 = 17.104 F = MSR MSE