A food server records the total bill and the amount of the tip received by 5 individuals who dined alone. Here are the data: Total $4.50 $5.79 $6.25 $4.62 $6.35 Tip $0.75 $1.00 $0.75 $0.58 $1.00 (a) Is there a clear explanatory variable and response variable in this setting? If so, tell which is which. If not, explain why not. b) Make a scatterplot of these data on your work document. (c) Based on the scatterplot, describe the relationship between the total bill and tip received for these 5 customers. (d) The correlation r between the total bill and tip received is r = 0.67. Explain how this confirms the description from part (c). (e) How would r change if all the total bill amounts were reduced by 10%? tip received was measured in cents rather than dollars? (f) Suppose another customer whose total bill was $5.15 tipped $0.75. How would including this point influence r? Justify your answer without performing any calculations.

Creating a linear regression model of the given data, the necessary deductions required to solve the problems posed. Hence, the solutions are as follows :

A.)

The explanatory variable is not very obvious as we have similar measured or predicted value for two different data points in the data.

B.)

The scatterplot of the relationship is attached with Total being the independent and tips being the dependent variable.

C.)

The scatter plot shows a positive association or relationship between total and tips.

D.)

The Correlation Coefficient gives the strength and direction of the relationship between two variables. Hence, 0.67 is positive and shows a fairly strong association.

E.)

A reduction in total bill by 10% would still depict an increase in the tips as based on the total bill amount.

If tips was measured in cent and not dollars, then, the the value of r will remain the same, as the unit of a variable has no effect on the correlation Coefficient.

F.)

The addition of a point with total bill of 5.15 and tip amount of 0.75 will strengthen the existing relationship. Hence, the value of R will increase slightly.

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(a) There is not a clear explanatory variable and response variable

(b) Please find attached the scatterplot created with Microsoft Excel

(c) There is some relationship between the total bill and tip received

(d) The correlation value of r = 0.67, reaffirm that there is an amount of positive correlation between the total bill and the tip received

(e) The correlation will remain positive, and will increase

(ii) The correlation will remain constant

(f) The correlation and r will increase marginally

Step-by-step explanation:

(a) The given parameters are;

Total                   Tip

$4.50                 $0.75

$5.79                 $1.00

$6.25                 $0.75

$4.62                 $0.58

$6.35                 $1.00

From the given data, the relationship between the variables are not clear as the lowest and the second highest total give the same amount as tip, the second lowest receive the lowest tip and the median value of the total and the highest value give the same value of tip

Therefore, there is not a clear explanatory variable and response variable

(b) Please find attached the scatterplot

(c) Based on the scatterplot, as the total bill increases, the response the tip increases, therefore, there is some relationship between the total bill and tip received

(d) The correlation value of r = 0.67, reaffirm that there is an amount of positive correlation between the total bill and the tip received

(e) (i)Whereby the total bill were reduced by 10% each, we have, that the correlation will remain positive, and will increase

(ii) Whereby the tip received were measured in cents rather than dollars, the correlation will remain constant

(f) When the total bill of another customer whose bill is $5.15 and tipped $0.75 is added, we have three customers out of six that give an equal tip, therefore, the correlation and r will increase marginally