Michigan State University researchers want to investigate how rainfall affects t

Question

Michigan State University researchers want to investigate how rainfall affects the yield of crops in East Lansing. The researchers found that the annual mean amount of rainfall is about 242 inches and the standard deviation is about 18.8 inches. The mean yield of crops in East Lansing is about 272 tonnes with a standard deviation of 40 tonnes. The correlation between the amount of rainfall and yield of crops is about 0.5 To predict yield amount, the MSU researchers decided to use a regression line of the form: yield = bo +bl* rainfall. The estimated slope of the regression line is: [Answer to 2 decimal places] Tries 0/5 Tries 0/5 Tries 0/5 Submit Answer The estimated intercept of the regression line is: [Answer to 2 decimal places] The predicted value of the yield of crop (in tonnes) when the amount of rainfall is 255 inches is: [Answer to 2 decimal places] Suppose in a certain year, the amount of rainfall is 255 inches and the yield of crop is 285 tonnes. The residual value of the yield of crop (in tonnes) is: [Answer to 2 decimal places] Submit Answer Submit Answer Tries o/5 Submit Answer About what percentage of the total sample variation in yield of corp is explained by the regression model? [Answer to 1 decimal place] Submit Answer Tries 0/5

Explanation / Answer

estimate slope =r*Sy/Sx =0.5*40/18.8=1.06

estimate intercept =272-1.06*242=15.48 ( Please try 14.55 if this comes wrong)

predicted value =15.48+1.06*255=285.78 ( Please try 284.85 if this comes wrong)

residual =285-285.78 =-0.78 ( Please try 0.15 if this comes wrong)

% of variation =(0.5)2*100 =25.0%

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