A researcher is interested in using multiple regression to study the factors that determine the overall satisfaction for Brand X. The factors that the researcher has identified are product quality (X1 packaging (x2), and customer service (X3). The following results were obtained: ANOVA df SS MS F Regression 3 78.055 26.018 16.011 Residual 26 16 1.625 Total 29 94.055 R Square: 0.663 Coefficients Standard Error t Stat Intercept 0.273 2.310 0.118 Product quality 0.692 0.188 3.688 Packaging -0.244 0.319 -0.763 Customer service 0.626 0.189 3.305 a) Write down the multiple regression equation. (2 marks) b) Interpret the meaning of the coefficient of determination. (2 marks) c) Interpret the meaning of the slope coefficients for product quality and packing service (4 marks). d) Write down another potential independent variable that could be included in the analysis (2 marks). e) Predict the overall satisfaction if the product quality score is 3, packaging score is 5 and customer service score is 8. (2 marks) f) Is the overall model significant at the 5% level of significance? (4 marks) 9) Which regression coefficients are significant at the 5% level of significance? (4 marks)\fThe president of Small Business Australia believes that the number of owner-managers of unincorporated businesses in Australia ('000s) has been evidenceing an exponential trend since 2004. He uses Microsoft Excel to obtain the output below. The dependent variable is the log base 10 of the number of owner-managers, while the independent variable is period, where 2004 is coded as 1, 2005 is coded as 2, etc. Model is given by: Logo(Owner Managers,) = Bo+By(period.)+et SUMMARY OUTPUT Regression Statistics Multiple R 0.9913 R Square 0.9827 Adjusted R Square 0.9817 Standard Error 0.0265 Observations 18 ANOVA df SS MS F Regression 1 0.6417 0.6417 911.2983 Residual 16 0.0113 0.0007 Total 17 0.6529 Coefficients Standard Error t Stat P-value Intercept 2.4977 0.0130 191.4105 0.0000 period 0.0364 0.0012 30.1877 0.0000 Calculate the forecast for demand in 2025.Given below are Excel outputs for various estimated autoregressive models for the number of people employed on a full-time basis (in thousands) from January 2019 through June 2022. You are also given that the number of people employed on a full-time basis for April, May and June for 2020 are 8012, 8061 and 8018 in thousands respectively. First-Order Autoregressive (AR1) Model: Coefficients Standard Error t Stat P-value Intercept 6539.477 1261.347 5.185 0.000 LAG_1 0.181 0.158 1.145 0.260 Second-Order Autoregressive (AR2) Model: Coefficients Standard Error t Stat P-value Intercept 3265.098 1392.402 2.345 0.025 LAG_1 0.072 0.139 0.520 0.606 LAG_2 0.519 0.139 3.735 0.001 Third-Order Autoregressive (AR3) Model: Coefficients Standard Error t Stat P-value Intercept 1848.437 1308.410 1.413 0.167 LAG_1 -0.175 0.056 -3.113 0.002 LAG_2 0.473 0.124 3.815 0.001 LAG_3 0.472 0.145 3.252 0.003 Fourth-Order Autoregressive (AR4) Model: Coefficients Standard Error t Stat P-value Intercept 2013.032 1323.469 1.521 0.138 LAG_1 -0.095 0.169 -0.558 0.580 LAG 2 0.551 0.150 3.667 0.001 LAG_3 0.445 0.148 3.009 0.005 LAG 4 -0.153 0.166 -0.921 0.364 a. Using a 5% level of significance, what is the appropriate autoregressive model for number of people employed on a full-time basis? Fully explain your answer. (3 marks) b. If one decides to use the Third-Order Autoregressive model, what will be the predicted number of people employed on a full-time basis for July 2022? (3 marks)The Priority Time Management course is designed to save managers from wasting time on taslG. such as checking emails. The following data shows the amount of time in minutes spent checking emails for a sample of six managers both before and after attending the course. Manager Before After 1 23 18 2 45 23 3 67 50 4 34 21 5 12 13 6 60 45 At the 0.01 level of signicance is there any evidence that the course has reduced the amount of time managers spend checking emails