Question

In: Statistics and Probability

A Regression analysis was applied between sales data (y in $1000s) and advertising expenditure (x in...

  1. A Regression analysis was applied between sales data (y in $1000s) and advertising expenditure (x in $100s) and the estimated regression equation is obtained as ŷ = 12 + 1.8 x.
    Suppose SST=300, SSE=75, sb1 =0.2683 and ?=17

    1. a) Carry out a t-test to see whether the advertising expenditure is significant. Use α = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps.

    2. b) Carry out an F-test to see whether the advertising expenditure is significant. Use α = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps.

Solutions

Expert Solution


Related Solutions

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s)...
Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. ​ = 30 + 2x ​ n = 17 SSR = 450 SSE = 150 The critical t value for testing the significance of the slope, at a .05 level of significance, is: 1.746. 2.131. 1.753. 2.120.
A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the...
A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the following. Regression Statistics Multiple R 0.8800 R Square 0.7744 Adjusted R Square 0.7560 Standard Error 232.29 Observations 25 ANOVA df SS MS F Significance F Regression 3 53184931.86 17728310.62 328.56 0.0000 Residual 21 1133108.30 53957.54 Total 24 54318040.16 Coefficients Standard Error t Stat P-value Intercept 927.23 1229.86 0.75 0.4593 Advertising (X1) 1.02 3.09 0.33 0.7450 Price (X2) 15.61 5.62 2.78 0.0112 Time (X3) 170.53...
A regression analysis relating a company’s sales, their advertising expenditure, price (per unit), and time (taken...
A regression analysis relating a company’s sales, their advertising expenditure, price (per unit), and time (taken per unit production) resulted in the following output. Regression Statistics Multiple R 0.9895 R Square 0.9791 Adjusted R Square 0.9762 Standard Error 232.29 Observations ANOVA ​ df SS MS F Significance F Regression 3 53184931.86 17728310.62 328.56 0.0000 Residual 21 1133108.30 53957.54 Total 24 54318040.16 ​ ​ ​ Coefficients Standard Error t Stat P-value Intercept 927.23 1229.86 0.75 0.4593 Advertising (x1) 1.02 3.09 0.33...
A regression analysis of 32 months’ data relating a company's monthly advertising expenses (x, in thousands...
A regression analysis of 32 months’ data relating a company's monthly advertising expenses (x, in thousands of dollars) to its sales (y, in thousands of dollars) yields the following output: • ?0=100 • ?1=5.3 • Standard error of the estimate ? = ?? = 56 • Standard error for ?1, ???1 =0.3 Furthermore, when ? ∗=9, the standard error for a confidence interval for the estimated mean response is given by ???̂ = 29, while the standard error for a...
1-A regression analysis between weight (y in pounds) and height (x in inches) resulted in the...
1-A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: ?̂=120+5? This implies that if the height is increased by 1 inch, the weight is expected to: A. increase by 5 pounds B. increase by 24 pounds C. increase by 1 pound D. decrease by 1 pound If the coefficient of correlation is -0.60, then the coefficient of determination is: A. 0.36 B. -0.36 C. -0.60 D. 0.40 2- For...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years. Advertising Expenditure (in $10,000) (x) Sales in Millions of Dollars (y) 32 15 33 16 34 18 34 17 35 16 37 18 39 21 40 24 ​ a. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. b. Compute an estimated regression equation between sales and advertising. c. If the...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years. Advertising Expenditure (in $10,000) (x) Sales in Millions of Dollars (y) 32 15 33 16 34 18 34 17 35 16 37 18 39 21 40 24 ​ a. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. b. Compute an estimated regression equation between sales and advertising. c. If the...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years. Advertising Expenditure (in $10,000) (x) Sales in Millions of Dollars (y) 32 15 33 16 34 18 34 17 35 16 37 18 39 21 40 24 ​ a. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. b. Compute an estimated regression equation between sales and advertising. c. If the...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years. Sales in Millions of Dollars (y)                                       Advertising Expenditure (in $10,000) (x) 15                                                                                            32 16                                                                                            33 18                                                                                            35 17                                                                                            34 16                                                                                            36 19                                                                                            37 19                                                                                            39 24                                                                                            42 a. Use the method of least squares to compute an estimated regression equation between sales and advertising b. If the company's advertising expenditure is $400,000,...
9) Use the following data to estimate a linear regression equation between y and x. Interpret...
9) Use the following data to estimate a linear regression equation between y and x. Interpret the estimated slope coefficient. Predict y for an x value of 9. Calculate and interpret the model’s R-squared. x y 21 12 17 10 11 8 3 5 13 15
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT