Use the followingg to answer questions 5-7 ust choose the correct answer, no fur

Question

Use the followingg to answer questions 5-7 ust choose the correct answer, no further explanation is requi Suppose I have the following summary information:- n = 34, x = 43, y = 110, sx = 4.5, sy = 12.07, r--O.87, Min = 0 ,Maxx-67 5) Using the summary information, find the equation of the least-squares regression line that pertains to this information. a) = 210.19-2.33x b) y = 299.11-2.33x c) = 210.19 + 2.33x d) =189 0.32x 6) Using the equation calculated in the previous question, find the estimated y value (y-hat) when x = 80 a) 23.66 b) 397.0:3 c) 112.63 d) You cannot find the value of the estimated y value when the x value being used to estimate is outside the range of original x values (called extrapolation) 7) According to the summary information, r-0.87 This is the correlation coefficient telling us about the strength and direction of the linear relationship between x and y. What is r2 and what does it tell us about our model? a) r2=75.69%. Meaning 75.69% of the variation is explained by the linear relationship between x and y b) r2=24.31%. Meaning 24.31% of the variation is explained by the linear relationship between x and y c) r2=-87%. Meaning-87% of the variation is explained by the linear relationship between x and y d) r2=100%. Meaning 100% of the variation is explained by the linear relationship between x and y

Explanation / Answer

(5)

Slope of regression line, m = r*(sy/sx) = -0.87*(12.07/4.5) = -2.33

intercept, c = y'-(m*x') = 110-((-2.33)*43) = 210.19

So the regression line is:

y = 210.19 - 2.33*x

(6)

Putting x=80 in the above equation, we get:

y = 210.19 - 2.33*80 = 23.79

(7)

Since r = -0.87, so r2 = 0.7596 = 75.69%. So this means that 75.69% of the variation is explained by the regression line.

Hope this helps !

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