Question

problem 1
a waiter is trying to predict how much he will receive in tips. he has recorded the meal cost and amount of tip left for his last few tables.

regression equation:

if the next table orders a meal costing $11.00, how much tip should he expect to receive?

if the next table orders a meal costing $31.50, how much tip should he expect to receive?

Explanation:

Step1: Calculate the regression equation (using a statistical software or calculator with regression - function)

Let \(x\) be the meal cost and \(y\) be the tip. Using a calculator or software (e.g., TI - 84 Plus: Stat, Edit to enter data, then Stat, Calc, LinReg(ax + b)), assume the regression equation is \(y=ax + b\). After inputting the data \((x_1,y_1)=(4.75,0.80),(x_2,y_2)=(6.84,0.90),(x_3,y_3)=(12.82,1.80),(x_4,y_4)=(20.42,3.00),(x_5,y_5)=(8.97,1.00)\), we get \(a\approx0.12\) and \(b\approx0.2\). So the regression equation is \(y = 0.12x+0.2\).

Step2: Predict tip for \(x = 11.00\)

Substitute \(x = 11.00\) into the regression equation \(y=0.12x + 0.2\).
\(y=0.12\times11.00+0.2=1.32 + 0.2=1.52\)

Step3: Predict tip for \(x = 31.50\)

Substitute \(x = 31.50\) into the regression equation \(y=0.12x+0.2\).
\(y=0.12\times31.50+0.2=3.78+0.2 = 3.98\)

Answer:

Regression Equation: \(y = 0.12x+0.2\)
For a meal costing $11.00, the expected tip is $1.52.
For a meal costing $31.50, the expected tip is $3.98.