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
Step by step
Solved in 2 steps
- Use the following linear regression equation to answer the questions. X3=-17.3+3.7x1+9.6x4-2.0x7 a) which number is the constant term? List the coefficient explanatory variables. constant= x1 coefficient = x4 coefficient =x7 coefficient =b) if x1=1, x4=-3, x7=5, what is the predicted value for x3?(round you answer to one decimal place.) c) suppose x1 and x7 were held at fixed but arbitrary values. If x4 increased by 1 unit what would we expect the corresponding change in x3 to be? if x4 increased by 3 units what would be the corresponding expected change in x3?if x4 decreased by 2 units what would we expect for the corresponding change in x3?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 ofIf X= 6 + 20Y, then as per your Regression equation analysis what is the value of a? O a. 26 O b. 20 O c. 14 O d. 6
- Use the table and the given regression equation to answer parts (a)-(e). 3 y=4-4x -8 X y SSE= No Yes 1 0 a. Compute the three sums of squares, SST, SSR, and SSE, using the defining formulas. SST = (Type an integer or a decimal.) SSR = (Type an integer or a decimal.) (Type an integer or a decimal.) b. Verify the regression identity, SST = SSR + SSE. Is this statement correct? 20 O A. Not useful -4 c. Determine the value of r2², the coefficient of determination. 2 (Round to four decimal places as needed.) d. Determine the percentage of variation in the observed values of the response variable that is explained by the regression. % (Round to two decimal places as needed.) e. State how useful the regression equation appears to be for making predictions.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 72Use 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…
- 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. $The 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 winsThe number of hours 6 students spent for a test and their scores on that test are shown below:Given are five observations for two variables, and y. a. Choose the correct scatter diagram for these data: A. C. D 60 50 40 30- 20 -10- 60 50 40 -30 20 10- 10 10 20 20 30 30 40 40 50 50 60 x 60 x B. D. 60 50 40 30 20 10- 60 50 40 30- 20 10- 10 10 20 20 30 30 40 40 50 50 60 x 60 x 5 15 8 23 19 Xi Yi 55 40 50 15 25 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x and y. and y by drawing a straight line through the data. c. Try to approximate the relationship between Many different straight lines can be drawn ✔ to provide a linear approximation of the relationship between x and y.
