Question

Employees	Age	Salary
Mary	23	28.6
Frieda	31	53.3
Alicia	44	73.8
Tom	22	26.0
Gillian	25	34.3
Bob	54	63.5
Vivian	51	96.4
Cacil	60	122.9
Barry	40	63.8
Jaime	64	111.1
Wanda	34	82.5
Sam	63	80.4
Saundra	40	69.3
Pete	31	52.8
steve	28	54.0
Juan	36	58.7
Dave	58	72.3
Lee	52	88.6
Judd	43	60.2
Sunil	28	61.0
Marcia	54	75.8
Ellen	44	79.8
Iggy	36	70.2

1. Can we conclude that employee age helps in predicting average employee salary? Follow the 7 steps for hypothesis testing. (10 points)
2. Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)
3. Find the coefficient of determination, and interpret its value. (3 points)
4. Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)
5. Estimate with 95% confidence the average employee salary for all employees that are 35 years old. Predict with 95% confidence the estimated salary for an individual employee that is 35 years old. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (6 points)
6. Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t² = F. (3 points)
7. Attach or include the relevant Minitab output. (6 points)

Answer 1

The regression output is:

Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)

The regression equation is:

Salary = 8.1906 + 1.4474*Age

The constant is meaningless since age cannot be zero

The coefficient age interprets that when age increases by 1, the salary will increase by 1.4474.

Find the coefficient of determination, and interpret its value. (3 points)

The coefficient of determination value is 0.663. It means that 66.3% of the variation in Salary is explained by Age.

Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)

The residual output is:

Observation	Salary	Predicted	Residual
1	28.60	41.48	-12.88
2	53.30	53.06	0.24
3	73.80	71.87	1.93
4	26.00	40.03	-14.03
5	34.30	44.37	-10.07
6	63.50	86.35	-22.85
7	96.40	82.01	14.39
8	122.90	95.03	27.87
9	63.80	66.09	-2.29
10	111.10	100.82	10.28
11	82.50	57.40	25.10
12	80.40	99.37	-18.97
13	69.30	66.09	3.21
14	52.80	53.06	-0.26
15	54.00	48.72	5.28
16	58.70	60.30	-1.60
17	72.30	92.14	-19.84
18	88.60	83.45	5.15
19	60.20	70.43	-10.23
20	61.00	48.72	12.28
21	75.80	86.35	-10.55
22	79.80	71.87	7.93
23	70.20	60.30	9.90

The residual plot is:

From the residual plot, it is clear that the data is linearly related and there is a linear relationship between Age and Salary.

Estimate with 95% confidence the average employee salary for all employees that are 35 years old. Predict with 95% confidence the estimated salary for an individual employee that is 35 years old. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (6 points)

Predicted values for: Salary
		95% Confidence Interval		95% Prediction Interval
Age	Predicted	lower	upper	lower	upper	Leverage
35	58.8483	52.0302	65.6665	29.1281	88.5685	0.056

The 95% confidence interval of the average employee salary for all employees that are 35 years old is between 52.0302 and 65.6665. It includes the predicted value of the average employee salary for all employees that are 35 years old.

The 95% prediction interval of the average employee salary for all employees that are 35 years old is between 29.1281 and 88.5685. It includes the predicted value of the average employee salary for all employees that are 35 years old.

Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t² = F. (3 points)

The P-value for the slope is the same for the F and t statistic which is 0.000.

t = 6.42

t² = 6.42² = 41.25 which is equal to F.

All Minitab outputs are attached.