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?

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:

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:

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:*

*H*0: r = 0

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

*Alternative hypothesis:*

*H*a: 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...

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