A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. The following data were recorded: Advertising Costs ($) 40 Sales ($) 385 20 400 25 395 20 365 475 30 50 440 40 490 20 420 50 560 525 40 25 480 50 510 a) Plot a scatter diagram, you may use Excel. (5 marks) b) Find the equation of the regression line to predict weekly sales from advertising expenditures. (6 marks) c) Estimate the weekly sales when advertising costs are $35. (2 marks) d) Plot the residuals versus advertising costs. Comment. (5 marks) e) Using the t-test, test the hypothesis that 6 against the alternative that B< 6. Use a 0.025 level of significance. (10 marks) f) Construct a 95% confidence interval for the average weekly sales when $45 is spent on advertising. (5 marks) g) Construct a 95% prediction interval for the average weekly sales when $45 is spent on advertising (5 marks) h) What is the percentage of variations in weekly sales explained by the advertising costs? (2 marks)

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05-12-2022
Mathematics

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A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. The following data were recorded: Advertising Costs ($) 40 Sales ($) 385 20 400 25 395 20 365 475 30 50 440 40 490 20 420 50 560 525 40 25 480 50 510 a) Plot a scatter diagram, you may use Excel. (5 marks) b) Find the equation of the regression line to predict weekly sales from advertising expenditures. (6 marks) c) Estimate the weekly sales when advertising costs are $35. (2 marks) d) Plot the residuals versus advertising costs. Comment. (5 marks) e) Using the t-test, test the hypothesis that 6 against the alternative that B< 6. Use a 0.025 level of significance. (10 marks) f) Construct a 95% confidence interval for the average weekly sales when $45 is spent on advertising. (5 marks) g) Construct a 95% prediction interval for the average weekly sales when $45 is spent on advertising (5 marks) h) What is the percentage of variations in weekly sales explained by the advertising costs? (2 marks)

Sagot :

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PratikshaS PratikshaS · Answer 1 · 2022-12-08T02:20:03-05:00

For given data,

a) A scatter diagram is as shown below.

b) the coefficient of correlation is, r = 0.63

c) the linear regression equation (least-squares equation of the line) to predict weekly sales from advertising expenditures is : y = 3.2208x + 343.71, where x is the Advertising Costs and y be the Sales in dollars

d) when advertising costs are $32, the weekly sales would be 446.78 dollars.

In this question, we have been given that a retail merchant made a study to determine the relation between weekly advertising expenditures and sales.

The following data were recorded:

Advertising Costs, $ 40 20 25 20 30 50 40 20 50 40 25 50

Sales, $ 385 400 395 365 475 440 490 420 560 525 480 510

a) a scatter plot for the above data is as shown below.

b) the coefficient of correlation is:

r = √0.403

r = 0.63

c) the linear regression equation is:

y = 3.2208x + 343.71

where x is the weekly Advertising Costs and y be the Sales in dollars

d) the weekly sales when advertising costs are $32:

y = 3.2208(32) + 343.71

y = 446.78

So, when advertising costs are $32, the weekly sales would be 446.78 dollars.

Therefore, for given data:

a) A scatter diagram is as shown below.

b) the coefficient of correlation = 0.63

c) the linear regression equation: y = 3.2208x + 343.71

d) when advertising costs are $32, the weekly sales would be 446.78 dollars.

Learn more about the scatter plot here:

https://brainly.com/question/29231735

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Sagot :

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