A Counselor Working with Teenagers Is Interested in the Relationship

Essay

A counselor working with teenagers is interested in the relationship between anxiety and depression.The counselor administers a depression and anxiety test to each teenager.The scores obtained from the administration of the two inventories are given below. $$\begin{array} { | c | c | } \hline \text { Anxiety } & \text { Depression } \\\hline 22 & 16 \\\hline 12 & 8 \\\hline 68 & 33 \\\hline 10 & 6 \\\hline 5 & 5 \\\hline 53 & 24 \\\hline 44 & 18 \\\hline 37 & 17 \\\hline 0 & 2 \\\hline 21 & 14 \\\hline 64 & 31 \\\hline 33 & 17 \\\hline 55 & 30 \\\hline 18 & 13 \\\hline 3 & 3 \\\hline 4 & 4 \\\hline 11 & 7 \\\hline 13 & 9 \\\hline 7 & 5 \\\hline\end{array}$$
$\begin{array}{lrr} \text { The summary statistics are }\\& \text { Anxiety } & \text { Depression } \\\text { Sample mean } & 25.2632 & 13.7895 \\\text { Standard deviation } & 21.9895 & 9.8464\end{array}$

$\sum_{i=1}^{19}\left(x_{1}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=3828.0526$
a.If anxiety is the independent variable and depression is the dependent variable,what is the sample regression function? What do the estimated slope and intercept mean in context of this problem?
b.What is R-squared and what does it mean?
c.If an individual had an anxiety score of 40,what is their predicted level of depression?