A study of the tipping habits of restaurant-goers was completed.The data for two of the variables—x, the amount of the restaurant check, and y, the amount left as a tip for the servers—were used to construct a scatter diagram.
a. Do you expect the two variables to show a linear relationship? Explain.
b. What will the scatter diagram suggest about linear correlation? Explain.
c. What value do you expect for the slope of the line of best fit? Explain.
d. What value do you expect for the y-intercept of the line of best fit? Explain. The data are used to determine the equation for the line of best fit: yˆ =0.02 -0.177x
e. What does the slope of this line represent as applied to the actual situation? Does the value 0.177 make sense? Explain.
f. What does the y-intercept of this line represent as applied to the actual situation? Does the value 0.02 make sense? Explain.
g. If the next restaurant check was for $30, what would the line of best fit predict for the tip? h. Using the line of best fit, predict the tip for a check of $31.What is the difference between this amount and the amount in part g for a $30 check? Does this difference make sense? Where do you see it in the equation for the line of best fit?