Need help with these Regression problems, Please!
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(a) Use a = 0.01 to test the hypotheses Hzl : s2 = 0 H3131 andfor 32 is not equal to zero for the model y = Bo + 31x1 + 3212 + s, where X1 2 television advertising {$1,000s) X2 = newspaper advertising {$1,0005). Find the value of the test statistic. {Round your answer to two decimal places.) E Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject Ho. There is insufficient evidence to conclude that there is a significant relationship among the variables. O Do not reject H . There is sufficient evidence to conclude that there is a significant relationship among the variables. O Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables. O Do not reject H . There is insufficient evidence to conclude that there is a significant relationship among the variables. (b) Use a = 0.05 to test the significance of B 1. State the null and alternative hypotheses. O Ho: B , # 0 H, : B , =0 O Ho: B1 = 0 OHO: B, 0 O Ho: B1 = 0 H,: B, 0Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject H . There is insufficient evidence to conclude that , is significant. O Reject Ho. There is sufficient evidence to conclude that , is significant. O Do not reject H. There is sufficient evidence to conclude that B, is significant. O Do not reject Ho. There is insufficient evidence to conclude that , is significant. Should x, be dropped from the model? O Yes O No95 5|] 1.5 9D 2.9 2.0 95 4.9 1.5 92 2.5 2.5 95 3.u 3.3 94 3.5 2.3 94 2.5 4.2 94 3.n 2.5 The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x1), in thousands of dollars, and newspaper advertising (x2), in thousands of dollars. 111e estimated regression equation was i : 83.2 + 2.29;:1 + 1.302(2. (a) What is the gross revenue (in dollars} expected for a week when $5,000 is spent on television advertising (x1 = 5) and $1,500 is spent on newspaper advertising (x2 = 1.5)? (Round your answer to the nearest dollar.) $:l (b) Provide a 95% confidence interval (in dollars) for the mean revenue of all weeks with the expenditures listed in part (a). (Round your answers to the nearest dollar.) $|:|t0$|:| (1:) Provide a 95% prediction interval (in dollars) for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a). (Round your answers to the nearest dollar.) last\": The estimated regression equation for a model involving two independent variables and 10 observations follows. (a) Interpret 11 in this estimated regression equation. 1/ = 26.19?0 + 0.5509X1 + 0491sz 0 bl = 0.5509 is an estimate of the change in y corresponding to a Z O O O :3- Hi:- i:- n II II Interpret 12 in this estimated regression equation. 0 O O O t:- t:- t:- t:- M II n II II {b} Predict y when x1 = 190 and x2 = 310. E 0.4910 is an estimate of the change in y corresponding to a 0.5509 is an estimate of the change in y corresponding to a ' 0.4910 is an estimate of the change in 5! corresponding to a ' 0.5509 is an estimate of the change in y corresponding to a ' 0.5509 is an estimate of the change in y corresponding to a ' 0.4910 is an estimate of the change in 5! corresponding to a ' 26.19?0 is an estimate of the change in 1/ corresponding to a 2 = 0.4910 is an estimate of the change in 5! corresponding to a ' 26.19?0 is an estimate of the change in y corresponding to a unit change in x2 when x1 is held constant. 1 unit change in x1 when x2 is held constant. '_ unit change in x2 when x1 is held constant. unit change in x when x is held constant. 1 2 unit change in x1 when )(2 is held constant. unit change in x2 when x1 is held constant. 1 unit change in x1 when x2 is held constant. unit change in x2 when x1 is held constant. unit change in x1 when x2 is held constant. unit change in x1 when x2 is held constant. A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures. y: 21 + 10xl + 312 where X1 = inventory investment ($1,000s) X2 = advertising expenditures ($1,0003) y = sales ($1,0005). (a) Predict the sales (in dollars) resulting from a $15,000 investment in inventory and an advertising budget of $11,000. $: (b) Interpret b1 and 12 in this estimated regression equation. Sales can be expected to increase by $ for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by $ for every dollar increase in advertising expenditure when inventory investment is held constant. The following estimated regression equation based on 1|] observations was presented. )7 = 29.1250 + 0.5406X1 + 0.4580X2 The values of SST and SSR are 6,?14.125 and 6,229.3?5, respectively. (a) (h) (d) Find SSE. Compute R2. (Round your answer to three decimal places.) Compute R32. (Round your answer to three decimal places.) 2 _ R... |:| Comment on the goodness of t. (For purposes ofthis exercise, consider a proportion large it it is at least 0.55.) O The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. 0 The estimated regression equation provided a good t as a large proportion of the variability in 1/ has been explained by the estimated regression equation. 0 The estimated regression equation did not provide a good t as a large proportion of the variability in y has been explained by the estimated regression equation. 0 The estimated regression equation did not provide a good t as a small proportion of the variability in V has been explained by the estimated regression equation. The following estimated regression equation based on 10 observations was presented. y = 27.1870 + 0.5505X, + 0.4980X2 Here, SST = 6,732.125, SSR = 6,223.375, S;, = 0.0815, and S, = 0.0567. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR = MSE = (b) Compute F and perform the appropriate F test. Use a = 0.05. State the null and alternative hypotheses. O Ho : B, > B2 H, : B. = P 2 O Ho: B1 0 O H : B , = 0 H: B , #0 Ho: B 1 20 O Ha: B, so O Ho: B1

Question

Need help with these Regression problems, Please!

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(a) Use a = 0.01 to test the hypotheses Hzl : s2 = 0 H3131 andfor 32 is not equal to zero for the model y = Bo + 31x1 + 3212 + s, where X1 2 television advertising {$1,000s) X2 = newspaper advertising {$1,0005). Find the value of the test statistic. {Round your answer to two decimal places.) E Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject Ho. There is insufficient evidence to conclude that there is a significant relationship among the variables. O Do not reject H . There is sufficient evidence to conclude that there is a significant relationship among the variables. O Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables. O Do not reject H . There is insufficient evidence to conclude that there is a significant relationship among the variables. (b) Use a = 0.05 to test the significance of B 1. State the null and alternative hypotheses. O Ho: B , # 0 H, : B , =0 O Ho: B1 = 0 OHO: B, 0 O Ho: B1 = 0 H,: B, 0Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject H . There is insufficient evidence to conclude that , is significant. O Reject Ho. There is sufficient evidence to conclude that , is significant. O Do not reject H. There is sufficient evidence to conclude that B, is significant. O Do not reject Ho. There is insufficient evidence to conclude that , is significant. Should x, be dropped from the model? O Yes O No95 5|] 1.5 9D 2.9 2.0 95 4.9 1.5 92 2.5 2.5 95 3.u 3.3 94 3.5 2.3 94 2.5 4.2 94 3.n 2.5 The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x1), in thousands of dollars, and newspaper advertising (x2), in thousands of dollars. 111e estimated regression equation was i : 83.2 + 2.29;:1 + 1.302(2. (a) What is the gross revenue (in dollars} expected for a week when $5,000 is spent on television advertising (x1 = 5) and $1,500 is spent on newspaper advertising (x2 = 1.5)? (Round your answer to the nearest dollar.) $:l (b) Provide a 95% confidence interval (in dollars) for the mean revenue of all weeks with the expenditures listed in part (a). (Round your answers to the nearest dollar.) $|:|t0$|:| (1:) Provide a 95% prediction interval (in dollars) for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a). (Round your answers to the nearest dollar.) last\": The estimated regression equation for a model involving two independent variables and 10 observations follows. (a) Interpret 11 in this estimated regression equation. 1/ = 26.19?0 + 0.5509X1 + 0491sz 0 bl = 0.5509 is an estimate of the change in y corresponding to a Z O O O :3- Hi:- i:- n II II Interpret 12 in this estimated regression equation. 0 O O O t:- t:- t:- t:- M II n II II {b} Predict y when x1 = 190 and x2 = 310. E 0.4910 is an estimate of the change in y corresponding to a 0.5509 is an estimate of the change in y corresponding to a ' 0.4910 is an estimate of the change in 5! corresponding to a ' 0.5509 is an estimate of the change in y corresponding to a ' 0.5509 is an estimate of the change in y corresponding to a ' 0.4910 is an estimate of the change in 5! corresponding to a ' 26.19?0 is an estimate of the change in 1/ corresponding to a 2 = 0.4910 is an estimate of the change in 5! corresponding to a ' 26.19?0 is an estimate of the change in y corresponding to a unit change in x2 when x1 is held constant. 1 unit change in x1 when x2 is held constant. '_ unit change in x2 when x1 is held constant. unit change in x when x is held constant. 1 2 unit change in x1 when )(2 is held constant. unit change in x2 when x1 is held constant. 1 unit change in x1 when x2 is held constant. unit change in x2 when x1 is held constant. unit change in x1 when x2 is held constant. unit change in x1 when x2 is held constant. A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures. y: 21 + 10xl + 312 where X1 = inventory investment ($1,000s) X2 = advertising expenditures ($1,0003) y = sales ($1,0005). (a) Predict the sales (in dollars) resulting from a $15,000 investment in inventory and an advertising budget of $11,000. $: (b) Interpret b1 and 12 in this estimated regression equation. Sales can be expected to increase by $ for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by $ for every dollar increase in advertising expenditure when inventory investment is held constant. The following estimated regression equation based on 1|] observations was presented. )7 = 29.1250 + 0.5406X1 + 0.4580X2 The values of SST and SSR are 6,?14.125 and 6,229.3?5, respectively. (a) (h) (d) Find SSE. Compute R2. (Round your answer to three decimal places.) Compute R32. (Round your answer to three decimal places.) 2 _ R... |:| Comment on the goodness of t. (For purposes ofthis exercise, consider a proportion large it it is at least 0.55.) O The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. 0 The estimated regression equation provided a good t as a large proportion of the variability in 1/ has been explained by the estimated regression equation. 0 The estimated regression equation did not provide a good t as a large proportion of the variability in y has been explained by the estimated regression equation. 0 The estimated regression equation did not provide a good t as a small proportion of the variability in V has been explained by the estimated regression equation. The following estimated regression equation based on 10 observations was presented. y = 27.1870 + 0.5505X, + 0.4980X2 Here, SST = 6,732.125, SSR = 6,223.375, S;, = 0.0815, and S, = 0.0567. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR = MSE = (b) Compute F and perform the appropriate F test. Use a = 0.05. State the null and alternative hypotheses. O Ho : B, > B2 H, : B. = P 2 O Ho: B1 0 O H : B , = 0 H: B , #0 Ho: B 1 20 O Ha: B, so O Ho: B1