Relationship between meal cost and tip
A food server at a restaurant keeps track of the cost of meals (excluding tip) and tips of
customers he serves. Below are the cost of meals (excluding tip) and the tip for 5 of his
customers.
Meal cost ($) 4.50 5.79 6.24 16.79 4.62
Tip ($)
0.65 0.85 0.95 0.00 0.70
1. What is the explanatory variable? the response?
2. What is the average cost of a meal including tip?
3. The food server, who has taken STAT 101, uses the data to come up with the following
least squares regression line:
Tˆip = 1.11 − 0.064 ∗ M eal
Using this line, what is the predicted tip for a meal costing $5.79? What is the residual
for this prediction?
4. What seems to be wrong with the least squares regression equation? Explain briefly.
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5. Below is a plot of residuals versus the meal cost. Circle any influential point(s) on the
plot and on the original data table. What makes the point(s) unusual? Remember to
answer this within the context of the problem.
6. If you removed the single most influential point from the data, how would the regression
line change? You DO NOT need to calculate the new slope and intercept. You DO
need to say how the new slope and intercept will be different from the current values
and briefly explain your reasoning.
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