Question

The table shows the time a patient spends at the dentist and the amount of the bill.





What is the correlation coefficient for the data in the table?


–0.93

–0.27

0.27

0.93

Answer 1

Answer-

Correlation coefficient for the data in the table was found to be 0.93.

Solution-

Taking the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable or output variable as the amount of the bill.

We know that,

$r=\frac{n(\sum xy)-\sum x \sum y}{\sqrt{[n\sum x^{2} -({\sum x})^{2}]\times [n\sum y^{2} -({\sum y})^{2}]}}$

Calculating the values from the table, then putting it in the formula

$r=\frac{4 \times 3130.9 \ - \ 6.45 \times 1473}{\sqrt{[4\times 12.3725 \ - \ 6.45^{2}][4 \times 877475 \ - \ 1473^2]}}$

$\Rightarrow r=0.929720561 \approx 0.93$

∴  Correlation coefficient for the data is 0.93.

Answer 2

The correlation coefficient for the data in the table would be 0.93. So, the correct option is A.

What is the correlation coefficient?

The correlation coefficient is used to measure the strong relationship between the two variables.

It is given that the first column is labeled time spent at the dentist (in hours) with entries 1.4, 2.7, 0.75, and 1.6.

The second column is labeled bill amount (in dollars) with entries 235, 867, 156, and 215.

The numbers between -1 and 1 should be one of the values related to the bill amount.

By assuming the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable as the amount of the bill.

Hence, The correlation coefficient for the data in the table was found to be 0.93.

To know more about correlation coefficient;

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