One part of Clare's job at an environmental awareness
organization is to answer the phone to collect
donations. The table shows the number of hours she
worked each week, x, and the amount of donations in
dollars, y, that the organization collected each week for
10 weeks.
The data in the scatter plot suggests a linear
association. A line to model the data is given by
y=12x + 41.
I
A Desmos graphing calculator has been provided on
the following slide.
a. Use the given linear model to complete the table with
the residuals.
b. Is the line given a reasonably good fit? Explain your
reasoning.
c. Explain the meaning of the slope of the line in this
situation.
D. Describe the correlation between the variables as either strong or weak and as either positive or negative. Explain your reasoning.
E. Clare’s boss sees the graph and tells her, “We certainly tend to bring in a lot more money when you’re working here! This graph proves you’re the cause of this increase in donations!” Do you agree with Clare’s boss? Explain your reasoning

(d) The correlation between the variables is positive because when the number of hours in increased the donation amount is also increasing. And when the correlation coefficient is calculated it came out to be r = 0.9963 suggesting strong co-relation.

(e) Yes we can agree with him as the correlation coefficient is strong.

Suggesting the donation will increase.

semsee45 semsee45 · Answer 2 · 2022-12-20T07:36:59-05:00

Answer:

A) See attachment 2 with completed table.

B) Yes

C) The predicted donations collected increases by $12 for each additional hour Claire works each week.

D) Strong positive correlation.

E) No

Step-by-step explanation:

Part A

In simple linear regression, the residual is the difference between the data point and the line.

To calculate each point’s residual:

substitute each x-value into the given equation for the line of best fit to find the predicted value.
find the difference between each point's actual value and the predicted value.

(See attached 2 - table).

Part B

The regression line is a reasonably good fit, as the distance between the actual scores and the predicted scores is minimal.

(See attachment 3 - graph).

Part C

Given line of best fit: y = 12x + 41

The slope of the line of best fit is 12.

It suggests that the predicted donations collected increases by $12 for each additional hour Claire works each week.

Part D

Correlation measures how closely two variables are linked.

If two variables are correlated, you can draw a line of best fit on the scatter plot.

The correlation of the given data is strong as the points on the scatter diagram are very close to being in a straight line.

The correlation between the given variables is positive, since the slope of the line of best fit is positive.

Part E

From the given data and analysis of correlation, it certainly appears that when Claire is working, the amount of donations increases. However, caution has to be exercised when writing about two variables that are correlated. The changes in one variable might not cause the changes in the other. They could be linked by a third factor, or it could just be coincidence. Therefore as "Correlation does not imply causation", the graph cannot definitively prove that Claire is the cause of the increase in donations, so I don't agree with Claire's boss.