Monium Ren John Joyce Bear LingLing Frank Bamboo eaten(kg) 9.70 4.60 7.50 1.60 5

Question

Monium Ren John Joyce Bear LingLing Frank Bamboo eaten(kg) 9.70 4.60 7.50 1.60 5.70 9.50 7.90 Time spent eating(hr) 7.00 4.20 7.80 1.20 9.70 7.60 8.90 In HW3, you (hopefully) found the sums of squares to be SSxx = 50.3171, SSxy = 37.2114, SSyy = 52.4143, the equation of the least squares line as yˆ = 1.7162 + 0.7395x, and the standard error as s = 2.2314. (a). Calculate the correlation coefficient r and interpret this value. (b). Find the coefficient of determination r2 and interpret this value. (c). Predict the average time spent eating for a (very hungry) panda who ate 12kg of bamboo, is this a valid prediction? Why or why not? (d). Predict the average time spent eating for a panda who ate 5kg of bamboo, is this a valid prediction? Why or why not? 3 Stat 3500 Section 7 Oct. 17 4/4 (e). Create a 95% confidence interval for the mean value of y at x = 5. (f). Create a 95% prediction interval for a new observation of y at x = 5. (g). Which interval is wider? Is this always the case? Why or why not?

Explanation / Answer

a. Correlation coefficient, r=Sxy/sqrt (Sxx*Syy)=37.2114/sqrt(50.3171*52.4143)=0.72

b. The coefficient of determination is R^2=r^2=0.5184

Around 51.84% variability in the model is accounted for variation in amount of bamboo eaten.

c. Substitute x in the regression equation with 12.

bamboo eaten=1.7162+0.7395*12=10.59 Kg. This is not a valid prediction as 12 has not been used in the x variable (bamboo eaten) while predicting the least square regression line.

d. Substitute x with 5.

bamboo eaten=5.41 Kg. This is a valid prediction as the value is within the range of predictor values.

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