the table shows the time a patient spends at the dentist and the amount of the bill. what is the correlation…

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? bill amount for time spent at the dentist\n| time spent at the dentist (in hours) | bill amount |\n| ---- | ---- |\n| 1.4 | $235 |\n| 2.7 | $867 |\n| 0.75 | $156 |\n| 1.6 | $215 |\n -0.93\n -0.27\n 0.27\n 0.93

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? bill amount for time spent at the dentist\n| time spent at the dentist (in hours) | bill amount |\n| ---- | ---- |\n| 1.4 | $235 |\n| 2.7 | $867 |\n| 0.75 | $156 |\n| 1.6 | $215 |\n -0.93\n -0.27\n 0.27\n 0.93

Answer

Explanation:

Step1: Recall correlation coefficient formula

The correlation coefficient $r$ formula is complex and involves calculating means, standard - deviations, and sums of products. However, we can also use a calculator with a statistics function (like a TI - 84 Plus). Enter the data for time spent at the dentist ($x$ - values: $1.4,2.7,0.75,1.6$) and bill amount ($y$ - values: $235,867,156,215$) into the list editor of the calculator.

Step2: Calculate the correlation coefficient

On a TI - 84 Plus, go to STAT -> CALC -> LinReg(ax + b) and select the lists where the data is stored. The calculator will output several statistics, including the correlation coefficient $r$. When we perform these calculations for the given data, we find that as the time spent at the dentist increases, the bill amount also generally increases, indicating a positive correlation.

Answer:

$0.93$