Question

The table below shows the GPA and starting salary for 14 statistical analysts.

GPA	Starting Salary
2.07	47979
3.56	48758
3.17	48832
3.43	47592
1.12	45628
3.64	48971
1.96	46018
1.33	45164
2.62	46439
1.75	45446
3.86	50815
1.7	47075
3.48	48788
1.8	45747

a. Identify the scatter plot for the data.

Select your answer from one of the following options.

• a.Graph A
• b.Graph B
• c.Graph C

b. Use the Google Sheets command =CORREL to find the correlation coefficient r. Round your answer to 3 decimal places.

c. Use the commands =SLOPE and =INTERCEPT to find the line of best fit. Select the equation of the line of best fit from the choices below:Select your answer from one of the following options.

• a.y = 43418x + 2.54
• b.y = 0.03x - 0.06
• c.y = 2.54x + 47375
• d.y = 0.0005x - 20.8
• e.y = 1561x + 43418

d. Use the regression equation to predict the starting salary for a statistical analyst with a GPA of 3.48. Round your answer to the nearest whole dollar amount.

e. The data set includes an analyst that has a GPA of 3.48 and a starting salary of 48788. Using your answer to part c., calculate the residual for this analyst. Round your answer to the nearest whole dollar amount. Remember that residuals can be negative.

Answer 1

Answer(a):

We have the data

GPA	Starting Salary
2.07	47979
3.56	48758
3.17	48832
3.43	47592
1.12	45628
3.64	48971
1.96	46018
1.33	45164
2.62	46439
1.75	45446
3.86	50815
1.7	47075
3.48	48788
1.8	45747

The scatter plot of above data, taking GPA as independent variable on x-axis and starting salary on y-axis is as below:

You can choose the correct scatter plot which match with this scatter plot.

Answer(b):

The correlation coefficient between given two variables is

r=0.877

Hence the correlation coefficient between GPA and starting salary is 0.877

Answer(c):

In the given problem, we have starting salary as dependent variable (y) and GPA as independent variable (x).

So, we have to fit the following simple regression model:

The slope (b₁) of above model is

b₁ = 1561.025 ≈ 1561

The intercept of above model is

b₀ = 43417.94 ≈ 43418

So, the fitted model is

Hence the correct option is E. y = 1561x + 43418

Answer(d):

We have to predict the starting salary for a statistical analyst with a GPA of 3.48 using the above fitted regression model that means we have to predict y when x=3.48

Hence the predicted starting salary for a statistical analyst with a GPA of 3.48 is $48850

Answer(e):

We have an analyst that has a GPA of 3.48 and a starting salary of 48788 and the predicted salary for a statistical analyst with a GPA of 3.48 is 48850.

So the residual can be obtained as below:

Hence the residual is -62.

The excel commands are as below: