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The weight, in pounds, of a full backpack and the corresponding number of books in the backpack were recorded for each of 10 college students. The resulting data were used to create the residual plot and the regression output shown below Residual Number of Books DF Parameter Intercept Slope Estimate 10.53 0.53 Std. Er. 1.23 0. 46 Alternative 0 0 8 8 T 8 1 Stat. .57 .15 P.Value <0.0 0.2825 Which of the following values is closest to the actual weight, in pounds of the backpack for the student who had 4 books in the backpack? (A) 8 (B) 10 (C) 13 (D) 15 (E) 17

Respuesta :

Answer:

Option C is correct.

The value closest to the actual weight, in pounds of the backpack for the student who had 4 books in the backpack = 13

Step-by-step explanation:

The complete, correct question is presented in the attached image to this solution.

From the table, it is evident that

Intercept = 10.53

Slope = 0.53

Since, the residual plot is analysed with linear regression to obtain the linear relationship between actual weight of the backpack and the number of books in the backpack, the equation relating them must be

y = mx + c

where y = Actual weight of the backpack

m = slope obtained from the analysis = 0.53

x = number of books in the backpack

c = intercept obtained from the analysis = 10.53

So, the relationship is properly written as

y = 0.53x + 10.53

So, when the number of books in the backpack = 4, what is the actual weight of the backpack?

x = 4, y = ?

y = 0.53x + 10.53

y = (0.53×4) + 10 53 = 12.65

To the nearest whole number, 12.65 = 13

Hence, the value closest to the actual weight, in pounds of the backpack for the student who had 4 books in the backpack amongst the options = 13

Hope this Helps!!!

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