An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it...

 

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An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The firm has collected bivariate data on 15 of its recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y). For the data, the least-squares regression equation is y = 6.12 +0.17x. One client plans to spend about 4.3 million dollars on advertising and would like to know what kind of increase in sales she can expect after spending that amount. The firm has used the regression equation to predict the resulting percentage increase in sales for this client, but the firm also would like a prediction interval for the client's resulting percentage increase in sales and a confidence interval for the mean percentage increase in sales for dients spending this same amount. The firm has computed the following for its data: • mean square error (MSE) = 0.037; (4.3-) 1. = 0.2526, 15 15 i = 1 where x- X ,X1s denote the sample campaign costs, and x denotes their mean. Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below. (If necessary, consult a list of formulas.) Lower limit: 1. What is the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 4.3 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.) Upper limit: 2. Choose one response to answer the question below. the campaign cost is 4.3 million dollars. How would the confidence interval computed above compare to this prediction interval Tacciminn that hoth interuale are comnuted from the cama eamnle data17 Consider (but do not actually compute) the 95% prediction intervaj for an individual value for percentage increase in sales when Tems of Use Privacy I Ao www-awn.aleks.com/alekscgi/x/Isl.exe/1o_u-lgNslkr7j8P3jH-IBGBIH_OB3uhhqwxlXoS5SIQhuX6YjFjUgDFRvhXH9relMzlvv23_Pp32u8TfsHP_jUm65AJtEEbAJNv_rSkUZovRdKKoq?1oBw7QYjlbavbSPXtx-YCjsh_7mMmrc O CHI-SQUARE TESTS, INFERENCES FOR REGRESSION, AND ANOVA 三 Confidence intervals and prediction intervals from simple linear.. Emmanuel v (4.3-x) - 0.2526, 15 15 Σ i = 1 where x1, X2" ,X15 denote the sample campaign costs, and x denotes their mean. Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below. Aa (If necessary, consult a list of formulas.) Lower limit: 1. What is the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 4.3 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.) Upper limit: 2. Choose one response to answer the question below. Consider (but do not actually compute) the 95% prediction interval for an individual value for percentage increase in sales when the campaign cost is 4.3 million dollars. How would the confidence interval computed above compare to this prediction interval (assuming that both intervals are computed from the same sample data)? Choose one 3. Choose one response to answer the question below. For the campaign cost values in this sample, 2.1 million dollars is more extreme than 4.3 million dollars is, that is, 2.1 is farther from the sample mean campaign cost than 4.3 is. How would the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 2.1 million dollars compare to the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 4.3 million dollars? Choose one Explanation Check 2020 McGraw-Hill Education All Rights Reserved. Terms of Use | Privacy Accessibility O Type here to search An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The firm has collected bivariate data on 15 of its recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y). For the data, the least-squares regression equation is y = 6.12 +0.17x. One client plans to spend about 4.3 million dollars on advertising and would like to know what kind of increase in sales she can expect after spending that amount. The firm has used the regression equation to predict the resulting percentage increase in sales for this client, but the firm also would like a prediction interval for the client's resulting percentage increase in sales and a confidence interval for the mean percentage increase in sales for dients spending this same amount. The firm has computed the following for its data: • mean square error (MSE) = 0.037; (4.3-) 1. = 0.2526, 15 15 i = 1 where x- X ,X1s denote the sample campaign costs, and x denotes their mean. Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below. (If necessary, consult a list of formulas.) Lower limit: 1. What is the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 4.3 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.) Upper limit: 2. Choose one response to answer the question below. the campaign cost is 4.3 million dollars. How would the confidence interval computed above compare to this prediction interval Tacciminn that hoth interuale are comnuted from the cama eamnle data17 Consider (but do not actually compute) the 95% prediction intervaj for an individual value for percentage increase in sales when Tems of Use Privacy I Ao www-awn.aleks.com/alekscgi/x/Isl.exe/1o_u-lgNslkr7j8P3jH-IBGBIH_OB3uhhqwxlXoS5SIQhuX6YjFjUgDFRvhXH9relMzlvv23_Pp32u8TfsHP_jUm65AJtEEbAJNv_rSkUZovRdKKoq?1oBw7QYjlbavbSPXtx-YCjsh_7mMmrc O CHI-SQUARE TESTS, INFERENCES FOR REGRESSION, AND ANOVA 三 Confidence intervals and prediction intervals from simple linear.. Emmanuel v (4.3-x) - 0.2526, 15 15 Σ i = 1 where x1, X2" ,X15 denote the sample campaign costs, and x denotes their mean. Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below. Aa (If necessary, consult a list of formulas.) Lower limit: 1. What is the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 4.3 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.) Upper limit: 2. Choose one response to answer the question below. Consider (but do not actually compute) the 95% prediction interval for an individual value for percentage increase in sales when the campaign cost is 4.3 million dollars. How would the confidence interval computed above compare to this prediction interval (assuming that both intervals are computed from the same sample data)? Choose one 3. Choose one response to answer the question below. For the campaign cost values in this sample, 2.1 million dollars is more extreme than 4.3 million dollars is, that is, 2.1 is farther from the sample mean campaign cost than 4.3 is. How would the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 2.1 million dollars compare to the 95% confidence interval for the mean percentage increase in sales when the campaign cost is 4.3 million dollars? Choose one Explanation Check 2020 McGraw-Hill Education All Rights Reserved. Terms of Use | Privacy Accessibility O Type here to search