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

Explanation:

Step1: Recall correlation coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$, where $n$ is the number of data - points, $x$ is the independent variable (time spent at the dentist), and $y$ is the dependent variable (bill amount). Let $x_1 = 0.75,x_2=1.4,x_3 = 2.7,x_4=1.6$ and $y_1 = 156,y_2 = 235,y_3=867,y_4 = 215$, and $n = 4$.

Step2: Calculate sums

Calculate $\sum x=0.75 + 1.4+2.7+1.6=6.45$, $\sum y=156 + 235+867+215 = 1473$, $\sum xy=(0.75\times156)+(1.4\times235)+(2.7\times867)+(1.6\times215)=117+329+2340.9+344 = 3130.9$, $\sum x^{2}=0.75^{2}+1.4^{2}+2.7^{2}+1.6^{2}=0.5625 + 1.96+7.29+2.56 = 12.3725$, $\sum y^{2}=156^{2}+235^{2}+867^{2}+215^{2}=24336+55225+751689+46225 = 877475$.

Step3: Substitute into formula

$n(\sum xy)=4\times3130.9 = 12523.6$, $(\sum x)(\sum y)=6.45\times1473 = 9490.85$, $n\sum x^{2}=4\times12.3725 = 49.49$, $(\sum x)^{2}=6.45^{2}=41.6025$, $n\sum y^{2}=4\times877475 = 3509900$, $(\sum y)^{2}=1473^{2}=2169729$. Then $r=\frac{12523.6 - 9490.85}{\sqrt{(49.49 - 41.6025)(3509900 - 2169729)}}=\frac{3032.75}{\sqrt{7.8875\times1340171}}=\frac{3032.75}{\sqrt{10560301.625}}\approx\frac{3032.75}{3249.66}\approx0.93$.

Answer:

0.93