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a. Fit a linear regression equation
b. Compute for r
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- 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 follow. Weekly Gross Revenue ($1,000s) 96 90 ŷ = 95 92 95 94 94 94 Television Newspaper Advertising Advertising ($1,000s) ($1,000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let X₁ amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) ŷ = represent the (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly…assume the final regression equation from the stepwise regression analysis of the dependent variable cost (C) and the 10 potential independent variables is as follows: C = -5000 + 75 D + 0.4 S - 130 PT + 100 NE Given that the final model is valid, interpret the coefficient of NE: On average, a plant constructed in northeast region of USA costs _____ than a plant constructed in other regions, while keeping other variables constant A) 100 dollars more B) 100 millions of dollars more C) 100 millions of dollars less D) 100 dollars lessThe table shows the number of goals allowed and the total points earned (2 points for a win, and 1 point for an overtime or shootout loss) by 14 ice hockey teams over the course of a season. The equation of the regression line is y=−0.532x+211.813. Use the data to answer the following questions. (a) Find the coefficient of determination, r2, and interpret the result. (b) Find the standard error of the estimate, se, and interpret the result Goals Allowed, x Points, y215 112210 104217 103219 96259 85267 77281 51201 102214 99206 103216 94200 89263 70243 72
- Q12 a) Construct a regression model to determine the relationship between individual yearly income and the value of the car owned. b) Using the regression equation from (a) determine the value of the car if the yearly income is $40,000 c) Describe the relationship between yearly income and value of the car owned d) Identify the independent variable and dependent variable based on the regression model constructed in (a) e) Explain why it is incorrect to predict the value of the car if an individual income is $10,000A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: Cups of coffee (n) 1 1 2 3 4 5 5 People (P) 12 10 10 6 6 4 2 3 (a) Using regression to find a linear equation for P(n). Round to 2 decimal places. P(n)= (b) How many cups of coffee should he drink so that no one will complain about his attitude? Round to one decimal place.An individual wants to determine how much money a boy scout earns from selling popcorn (Y-variable) based on the length of time (in days) that they went out selling (X-variable). Using the following linear regression equation Ŷ = 5 + 20X: a. State the value of the intercept AND the value of the slope (2 points) b. Based on the given regression equation, what can you determine about the direction of the relationship between X and Y (i.e. is it positive or negative)? (2 points) c. If a boy scout sells popcorn for 4 days, how much money is he predicted to earn? (2 points)
- Consider the linear regression model Y; = Bo + B1 X¡ + U¡ for each i in $10,000) and Y; represents the home size (measured in square feet). We run an OLS regression and get: 1,..., n withn = 1,000. X; represents the annual income of individual i (measured Bin = 43.2, SE(§ „) = 10.2, Bon = 700, SE(Bom) = 7.4. Suppose that we want to test Ho : B1 O against H1 : ß1 # 0 at 1% significance level. Assuming that the sample size is large enough, which one of the following is true about the p-value of this test? 43.2 The p-value can be computed as P(-| ), where is the standard Normal CDF 10.2 а. b. None of the answers 43.2 The p-value can be computed as (- ), where O is the standard Normal CDF 10.2 С. 43.2 d. The p-value can be computed as 20(-- ), where O is the standard Normal CDF 10.232 In one study, the simple linear regression equation was found to be y = - 2.65 + 3.23 * x. Accordingly, if the value of x is 1.55, what will be the value of y? a) -7.66 B) -2.36 NS) 7.66 D) 2.36 TO) 6.32answer b-d
- 3. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁?(d) Write out the regression equation. (Use 2 decimal places.) x1 = + x2 + x3 + x4 If x2 (production costs) and x4 (book sales) were held fixed but x3 (promotional costs) were increased by 0.7 million dollars, what would you expect for the corresponding change in x1 (box office receipts)? (Use 2 decimal places.)(e) Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.) t P-value β2 β3 β4 (f) Find a 90% confidence interval for each coefficient. (Use 2 decimal places.) lower limit upper limit β2 β3 β4Use the following linear regression equation to answer the questions. X1 = 1.2 + 3.6x2 - 7.6x3 + 2.5x4 (a) Which variable is the response variable? O x1 O X4 O x2 O x3 Which variables are the explanatory variables? (Select all that apply.) O x1 O X4 O X3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X3 coefficient X4 coefficient (c) If x2 = 8, X3 = 6, and x4 = 4, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. O If we hold all other explanatory variables as fixed constants, then we can look at…
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