s. In many fast food restaurants, there is a strong correlation between a menu i

Question

s. In many fast food restaurants, there is a strong correlation between a menu item's fat content (measured in grams) and its calorie content. We want to investigate this rela food menu items at a well-known fast food restaurant, the fat content and calone measured. We decide to fit the least-squares regression line to the data, W p. Using all of the th fat content (x) as the A scatterplot of the data (with regression line sion e and (v) as the included) and a summary of the data are provided. One of the menu grams of fat and 1410 calories. 107 items is a hamburger with 0.979 (correlation between x and y) 40.35 grams (mean of the values of x) 662.88 calories (mean of the values of y) = 27.99 grams (standard deviation of the values of x) = 324.90 calories (standard deviation of the values of y) What is TRUE about the regression line in this example? @ 95.8% of the response variables can be explained by the predictors. 97.9% of the variation is explained by the regression model. O The point (40.35, 662.88) lies on the regression line.

Explanation / Answer

We know that correlation coeficient r is the measure of correlation betwee twoo variables . Where as coefficient of determination is propoertion of the total variabilty of the response explained by the model. is R2 r=sxy/sqrt(sxx*syy) and R2=sxy2/sxx*syy therefore R2=0.9792=0.9598 i.e 95.98% therefore option 1 is true. where the values 40.35 and 662.88 are the mean values of all the data points of x and y variable and does not lies inthe regression line.

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