Question
Asked Jan 16, 2020
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Tips Using the bill/tip data, find the best predicted tip amount for a dinner bill of $100. What tipping rule does the regression equation suggest?

107.34
63.60
Bill (dollars)
Tip (dollars)
50.68
98.84
33.46
87.92
16.00
12.00
17.00
5.00
5.50
8.08
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107.34 63.60 Bill (dollars) Tip (dollars) 50.68 98.84 33.46 87.92 16.00 12.00 17.00 5.00 5.50 8.08

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Expert Answer

Step 1

Regression:

The regression analysis is conducted here by using EXCEL. The software procedure is given below:

  • Enter the data.
  • Select Data > Data Analysis > Regression> OK.
  • Enter Input Y Range as Tip (dollars).
  • Enter Input X Range as Bill (dollars).
  • Click OK.

The output using EXCEL is as follows:

Statistics homework question answer, step 1, image 1
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Step 2

From the output, regression equation is, Tip = –0.35+0.15(Bill).

Strategy for Predicting the y value:

Analyze the below mentioned conditions for predicting the y value.

 

  • In scatterplot, the regression line fits the point well.
  • The value of r indicates that there is a linear correlation between the variables.
  • The prediction value is not away from the range of the given sample data.

 

If the regression equation satisfies the above mentioned conditions, then the regression is said to be a good model. Here, substitute the given value of x into the regression equation to predict the value of y.

If the regression equation does not satisfy the above conditions, then the regression is not a good model. Here, the best predicted value of y is the value of.

The scatter diagram, along with the best fitted line (least-squares regression line) for the data is as follows:

Statistics homework question answer, step 2, image 1
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Step 3

The horizontal axis represents bill and the vertical axis represents tip.

From the plot, it is observed that the regression line fit the points well.

Correlation coefficient r:

The hypotheses are given below:

Null hypothesis:

H0: r = 0

That is, there is no linear correlation between the bill and tip amounts.

Alternative hypothesis:

Ha: r≠ 0

That is, there is a linear correlation between the bill and tip amounts.

Sample correlation coefficient:

The value of the sample correlation coefficient (r) can be obtained using Excel formula.

Enter the function, =CORREL(A2:A7,B2:B7).

Thus, the value of the sample correlation coefficient, r is 0.828.

Conclusion:

The P-value is 0.042 and the level of...

Statistics homework question answer, step 3, image 1
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