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

Answer

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$. Let $x$ be the time spent at the dentist (in hours) and $y$ be the bill amount. For the given data: $n = 4$ $x_1=1.4,y_1 = 235;x_2=2.7,y_2 = 867;x_3=0.75,y_3 = 156;x_4=1.6,y_4 = 215$ $\sum x=1.4 + 2.7+0.75 + 1.6=6.45$ $\sum y=235 + 867+156+215 = 1473$ $\sum xy=1.4\times235+2.7\times867+0.75\times156+1.6\times215$ $=329+2340.9 + 117+344=3130.9$ $\sum x^{2}=1.4^{2}+2.7^{2}+0.75^{2}+1.6^{2}$ $=1.96 + 7.29+0.5625+2.56=12.3725$ $\sum y^{2}=235^{2}+867^{2}+156^{2}+215^{2}$ $=55225+751689+24336+46225=877475$

Step2: Substitute values into the formula

$n(\sum xy)=4\times3130.9 = 12523.6$ $(\sum x)(\sum y)=6.45\times1473=9500.85$ $n\sum x^{2}=4\times12.3725 = 49.49$ $(\sum x)^{2}=6.45^{2}=41.6025$ $n\sum y^{2}=4\times877475=3509900$ $(\sum y)^{2}=1473^{2}=2169729$ $r=\frac{12523.6 - 9500.85}{\sqrt{(49.49 - 41.6025)(3509900 - 2169729)}}$ $=\frac{3022.75}{\sqrt{7.8875\times1340171}}$ $=\frac{3022.75}{\sqrt{10560070.475}}$ $=\frac{3022.75}{3249.626}$ $= 0.93$

Answer:

0.93