You may need to use the appropriate technology to answer this question. The following data represent...

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You may need to use the appropriate technology to answer this question. The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years NOTE: Pay close attention to units as you answer the questions below. Sales (in $1,000,000s) (v) 15 16 18 16 19 19 24 Advertising Expenditure (in $1.000s) (x) 330 330 340 350 360 360 380 430 (a) Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. The scatter diagram shows no apparent relationship between sales and advertising. O The scatter diagram shows a positive relationship between sales and advertising. The scatter diagram shows a negative relationship between sales and advertising. (b) Use the method of least squares to compute an estimated regression equation which uses advertising (x) to predict sales (y) P= (Round your numerical values to four decimal places) (c) What does the slope of the estimated regression line indicate? As the advertising expenditure goes up by $1,000, the sales are expected to by s (Give your answer in dollars, Round your answer to the nearest integer.) THE TOTES (d) Compute the coefficient of determination. (Round your answer to four decimal places) Fully interpret its meaning. (Give your answer as a percent. Round your answer to two decimal places) The value of the coefficient of determination tells us that (e) Compute the correlation coefficient. (Round your answer to four decimal places) (f) Use the F-test to determine whether or not the regression model is significant at a -0.05. State the null and alternative hypotheses. ⒸHO:₂0 H: 0 ⒸH₂:₂=0 H₂: ₂0 Ho: Po=0 H₂:0 ⒸHg² By zo H₂: A₁ <0 ⒸHOO Halo-o Find the value of the test statistic. (Round your answer to two decimal places) Find the p-value. p-value= (Round your answer to three decimal places) What is your conclusion? Do not reject Ho We can conclude that the model is significant. O Reject Ho. We can conclude that the model is significant. Beach Club Garde Autumn Communi % of the variability in 7 has been explained by the least squares line. Check out 2022 5 DU TRUL TEJELLTO E LOIT CUIUue unas une nouer is anymian O Reject Ho. We can conclude that the model is significant. Do not reject Ho. We cannot conclude that the model is significant. O Reject Ho. We cannot conclude that the model is significant. (9) Use the f-test to determine whether the slope of the regression model is significant at a = 0.05. State the null and alternative hypotheses. Hoi A₁ 20 H₂: A₁ <0 Ho: P₁0 H₂:₁0 Ho: Po=0 H₂: Do 0 Ho: ₁0 Ho: P₁0 O Ho: Po * 0 H₂: Po=0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. p-value= (Round your answer to four decimal places.) What is your conclusion? O Reject Ho. We cannot conclude that the slope is significantly different from zero. O Reject Ho. We can conclude that the slope is significantly different from zero. Do not reject Ho. We can conclude that the slope is significantly different from zero. O Do not reject Ho. We cannot conclude that the slope is significantly different from zero. (h) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars. (Round your answer to the nearest integer.) $ (h) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars. (Round your answer to the nearest integer.) (1) Develop a 95% confidence interval for predicting the average sales for the years when $400,000 was spent on advertising. Give your answers in dollars. (Round your answers to the nearest integer.) to $ (1) Develop a 95% prediction interval for predicting the sales for a specific year when $400,000 was spent on advertising. Give your answers in dollars. (Round your answers to the nearest integer.) to $ (K) Discuss the differences in your answers to parts (1) and (3) O The prediction interval is wider than the confidence interval, because there is more variability associated with predicting the sales for one year with an advertising expenditure of $400,000 than there is with estimating the mean sales for all years with an advertising expenditure of $400,000 The confidence interval is wider than the prediction interval, because there is less variability associated with predicting the sales for one year with an advertising expenditure of $400,000 than there is with estimating the mean sales for all years with an advertising expenditure of $400,000. O The confidence interval is wider than the prediction interval, because you use a different critical value when developing a prediction of the sales for one year with an advertising expenditure of $400,000 than when developing an estimate of the mean sales for all years with an advertising expenditure of $400,000. The confidence interval is wider than the prediction interval, because confidence intervals are used to predict values of y for new observations corresponding to given values of x, and prediction intervals give an estimate of the mean value of y for a given value of x. The prediction interval is wider than the confidence interval, because you use a different critical value when developing a prediction of the sales for one year with an advertising expenditure of $400,000 than when developing an estimate of the mean sales for all years with an advertising expenditure of $400,000. You may need to use the appropriate technology to answer this question. The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years NOTE: Pay close attention to units as you answer the questions below. Sales (in $1,000,000s) (v) 15 16 18 16 19 19 24 Advertising Expenditure (in $1.000s) (x) 330 330 340 350 360 360 380 430 (a) Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. The scatter diagram shows no apparent relationship between sales and advertising. O The scatter diagram shows a positive relationship between sales and advertising. The scatter diagram shows a negative relationship between sales and advertising. (b) Use the method of least squares to compute an estimated regression equation which uses advertising (x) to predict sales (y) P= (Round your numerical values to four decimal places) (c) What does the slope of the estimated regression line indicate? As the advertising expenditure goes up by $1,000, the sales are expected to by s (Give your answer in dollars, Round your answer to the nearest integer.) THE TOTES (d) Compute the coefficient of determination. (Round your answer to four decimal places) Fully interpret its meaning. (Give your answer as a percent. Round your answer to two decimal places) The value of the coefficient of determination tells us that (e) Compute the correlation coefficient. (Round your answer to four decimal places) (f) Use the F-test to determine whether or not the regression model is significant at a -0.05. State the null and alternative hypotheses. ⒸHO:₂0 H: 0 ⒸH₂:₂=0 H₂: ₂0 Ho: Po=0 H₂:0 ⒸHg² By zo H₂: A₁ <0 ⒸHOO Halo-o Find the value of the test statistic. (Round your answer to two decimal places) Find the p-value. p-value= (Round your answer to three decimal places) What is your conclusion? Do not reject Ho We can conclude that the model is significant. O Reject Ho. We can conclude that the model is significant. Beach Club Garde Autumn Communi % of the variability in 7 has been explained by the least squares line. Check out 2022 5 DU TRUL TEJELLTO E LOIT CUIUue unas une nouer is anymian O Reject Ho. We can conclude that the model is significant. Do not reject Ho. We cannot conclude that the model is significant. O Reject Ho. We cannot conclude that the model is significant. (9) Use the f-test to determine whether the slope of the regression model is significant at a = 0.05. State the null and alternative hypotheses. Hoi A₁ 20 H₂: A₁ <0 Ho: P₁0 H₂:₁0 Ho: Po=0 H₂: Do 0 Ho: ₁0 Ho: P₁0 O Ho: Po * 0 H₂: Po=0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. p-value= (Round your answer to four decimal places.) What is your conclusion? O Reject Ho. We cannot conclude that the slope is significantly different from zero. O Reject Ho. We can conclude that the slope is significantly different from zero. Do not reject Ho. We can conclude that the slope is significantly different from zero. O Do not reject Ho. We cannot conclude that the slope is significantly different from zero. (h) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars. (Round your answer to the nearest integer.) $ (h) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars. (Round your answer to the nearest integer.) (1) Develop a 95% confidence interval for predicting the average sales for the years when $400,000 was spent on advertising. Give your answers in dollars. (Round your answers to the nearest integer.) to $ (1) Develop a 95% prediction interval for predicting the sales for a specific year when $400,000 was spent on advertising. Give your answers in dollars. (Round your answers to the nearest integer.) to $ (K) Discuss the differences in your answers to parts (1) and (3) O The prediction interval is wider than the confidence interval, because there is more variability associated with predicting the sales for one year with an advertising expenditure of $400,000 than there is with estimating the mean sales for all years with an advertising expenditure of $400,000 The confidence interval is wider than the prediction interval, because there is less variability associated with predicting the sales for one year with an advertising expenditure of $400,000 than there is with estimating the mean sales for all years with an advertising expenditure of $400,000. O The confidence interval is wider than the prediction interval, because you use a different critical value when developing a prediction of the sales for one year with an advertising expenditure of $400,000 than when developing an estimate of the mean sales for all years with an advertising expenditure of $400,000. The confidence interval is wider than the prediction interval, because confidence intervals are used to predict values of y for new observations corresponding to given values of x, and prediction intervals give an estimate of the mean value of y for a given value of x. The prediction interval is wider than the confidence interval, because you use a different critical value when developing a prediction of the sales for one year with an advertising expenditure of $400,000 than when developing an estimate of the mean sales for all years with an advertising expenditure of $400,000.

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