An engineer wants to determine how the weight of a car, x, affects gas mileage,
ID: 3087423 • Letter: A
Question
An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weight of various cars and their miles per Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Write the equation for the least-squares regression line, y^ = -.0066 x + 42.3360 (Round to four decimal places as needed.) Interpret the slope and intercept if appropriate. Choose the best interpretation for the slope. The slope indicates the average weight. The slope indicates the ratio between the average weight and the average miles per gallon. The slope indicates the average miles per gallon. The slope indicates the average change in miles per gallon for an increase of 1 pound in weight. It is not appropriate to interpret the slope because it is not equal to zero. Choose the best interpretation for the y-intercept. The y-intercept indicates the miles per gallon of the lightest car in the population. The y-intercept indicates the average weight for the population. The y-intercept indicates the miles per gallon for a new car. The y-intercept indicates the average miles per gallon for the population. It is not appropriate to interpret the y-intercept because it is outside the scope of the model. Predict the miles per gallon of car D and compute the residual. Is the miles per gallon of this car above average or below average for cars of this weight? The predicted value is miles per gallon. (Round to two decimal places as needed.)Explanation / Answer
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1.SLOPE=-0.00665...
IT INDICATES DECREASING FUNCTION , THAT IS WITH HEAVIER WEIGHT , A REDUCTION IN MILEAGE
D IS THE RIGHT CHOICE
2.INTERCEPT=42.336
E IS THE RIGHT CHOICE
3.MILES PER GALLON FOR CAR D IS 19.7 AS GIVEN .
AS PER FORMULA CALCULATION IT WILL BE
Y=42.33603-0.00665*3830 = 16.875
IT IS BELOW THE GIVEN VALUE OF 19.7 AS GIVEN
AND BELOW THE AVERAGE OF 19.74 FOR ALL THE MODELS
REGRESSION ANALYSIS T XI YI [XI -XM]^2 [YI -YM]^2 [XI-XM][YI-YM] 1 2665 26.6 538756 47.06 -5035 2 2925 20.8 224676 1.124 -502 3 3450 17.6 2601 4.58 -109 4 3830 19.7 185761 0.002 -17.2 5 4125 14 527076 32.95 -4167 SUM 16995 98.7 1478870 85.71 -9831 MEAN-M 3399 19.74 REGRESSION EQN. IS ….. Y=A+BX B= SUM[(XI-XM)*(YI-YM)] / SUM[(XI-XM)^2] -0.01 A= YM-B*XM 42.34 HENCE THE REGRESSION EQN. IS ….. Y = 42.33603 - 0.00665* X