Question

a professor feels that there is a relation between the number of hours a statistics student studies each week and the students age. she conducts a survey in which 26 statistics students are asked their age and the number of hours they study statistics each week. she obtains the accompanying results. complete parts (a) through (e). click the icon to view the data table.
\\(\hat{y}=0.231x+( - 0.908)\\) (round to three decimal places as needed.)
(c) find the least - squares regression line with the data point (35,8.1) removed
\\(\hat{y}=0.153x+(0.672)\\) (round to three decimal places as needed.)
(d) draw each least - squares regression line on the scatter diagram obtained in part (a) choose the correct graph.

Explanation:

Step1: Analyze regression - line equations

We have two regression - line equations: $\hat{y}=0.231x+( - 0.908)$ and $\hat{y}=0.153x + 0.672$. The first equation has a steeper slope ($m_1 = 0.231$) compared to the second ($m_2=0.153$), and a negative y - intercept in the first ($b_1=-0.908$) and a positive y - intercept in the second ($b_2 = 0.672$).

Step2: Examine scatter - diagram options

We need to look for a scatter - diagram where one line has a steeper positive slope and a negative y - intercept, and the other has a less steep positive slope and a positive y - intercept.

Step3: Identify the correct graph

By comparing the characteristics of the regression lines with the graphs, we can find the correct one.

Answer:

(No graphs are provided with specific details to choose from. But the general approach is to look for a graph where one line has a steeper positive slope and negative y - intercept and the other has a less steep positive slope and positive y - intercept.)