Question

The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks are entered into the Microsoft Excel Online file below. Use the XLMiner Analysis ToolPak to perform your regression analysis in the designated areas of the spreadsheet Open spreadsheet a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 2 decimals). Revenue = + TVAdv b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables (to 2 decimals). Revenue = + TVAdv + NewsAdv C. Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? d. Predict weekly gross revenue for a week when $4.9 thousand is spent on television advertising and $3.8 thousand is spent on newspaper advertising (to 2 decimals)? in thousands

Answer 1

Answer: A Bivariate Linear regression is a way to model the relationship between two variables. The equation has the form Y= a + b X, where Y is the dependent variable, X is the independent variable b is the slope of the line and a is the y-intercept.

where a = (sum(y)sum(x*x)-sum(x)sum(x*y))/(n*sum(x*x)-(sum(x)^2)) and

b = (n * sum(x*y)-sum(x)sum(y))/(n*sum(x*x)-(sum(x)^2))

found by the method of least squares

(a) Using the above formulas the developed estimated regression equation between revenue and television advertising comes out to be--

y_hat = 89.3 + 1.39 x where y_hat is the predicted value of the revenue and x = given value of the amount spent in television advertising.

A Multiple Linear regression is a way to model the relationship between more than two variables. The equation has the form Y= a + sum(bi Xi), where Y is the dependent variable, Xi's are the independent variable.

here for 2 variable case

b1 = (sum(x2*x2)sum(x1*y)-sum(x1*x2)sum(x2*y))/(sum(x1*x1)sum(x2*x2)-(sum(x1*x2)^2))

and b2 = (sum(x1*x1)sum(x2*y)-sum(x1*x2)sum(x1*y))/(sum(x1*x1)sum(x2*x2)-(sum(x1*x2)^2))

and a = ybar - b1x1bar - b2x2bar where ybar, x1bar, x2bar are the means of the three variables y , x1, x2.

found by the method of least squares

(b) Using the above formulas the developed estimated regression equation between revenue and television advertising and newspaper advertising comes out to be--

y_hat = 84.992 + 1.79 x1 + 1.164 x2 where y_hat is the predicted value of the revenue and x1 = given value of the amount spent in television advertising.and x2 = given value of the amount spent in newspaper advertisement

(c) No, the estimated regression equation coefficient of television advertising in (a) and (b) are not the same.

(d) The predicted weekly gross revenue for a week when 4.9 thousand is spent on television advertisement and 3.8 thousand is spent on newspaper advertisement is obtained by utting x1=4.9 and x2=3.8 in the regression equation obtained in part(b). It comes out to be y_hat = 98.186.