student obtained the following two regression equations. Do you agree with him? (1) 6X=15Y+21, (ii) 21X+14Y=56
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student obtained the following two regression equations. Do you agree with him?
(1) 6X=15Y+21,
(ii) 21X+14Y=56
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- Given the following regression equation, interpret the coefficients: y= 11 + 10x, - 7x2 +2.3x3 + e (a) An increase of 1 in x, leads to a change in y of (b) An increase of 2 in x, leads to a change in y of (c) A decrease of 0.2 in x3 leads to a change in y ofThe 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…The 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
- Use the following linear regression equation to answer the questions. X1 = 1.5 + 3.6x2 - 7.7x3 + 2.3x4 (a) Which variable is the response variable? O X4 O X2 O 3 Which variables are the explanatory variables? (Select all that apply.) O 3 O X4 O X1 O ×2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X, coefficient X4 coefficient (c) If x2 = 4, x3 = 9, and x4 = 10, what is the predicted value for x,? (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." O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall…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)The following estimated regression equation has been proposed to predict daily sales at a furniture store. ŷ = 12 − 5x1 + 8x2 + 17x3 where ŷ = estimated sales (in $1,000s) x1 = competitor's previous day's sales (in $1,000s) x2 = population within 1 mile (in 1,000s) x3 = 1 if any form of advertising was used; 0 otherwise (a) Fully interpret the meaning of the b3 coefficient (Give the answer in dollars.) Predict sales (in dollars) for the store with competitor's previous day's sale of $4,000, a population of 11,000 within 1 mile, and ... (b) no radio advertisements. $ (c) one radio advertisement. $ (d) eight radio advertisements. $
- answer b-dThe admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA. ŷ = −1.39 + 0.0234x1 + 0.00482x2 where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point average. #1)A high-school average 84 corresponds to x1 = 84 and a score of 535 on the SAT mathematics test corresponds to x2 = 535. Substitute these values into the estimated regression equation to find the final college GPA, rounding the result to two decimal places. GPA = −1.39 + 0.0234x1 + 0.00482x2 = -1.39 +0.0234 (_____________) + 0.00482 (535) = __________________If X 6 + 20Y, then as per your Regression equation analysis what is the value of a? О а. 6 ОБ. 26 O c. 14 O d. 20
- A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents the attendance (in thousands) and ŷ is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 17,000? 83.3 wins 98.5 wins 258.4 wins 263.3 wins(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 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Which variables are the explanatory variables? (Select all that apply.) x3 x1 x2 x4 (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 = 9, x3 = 3, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.)