Based on the table on the front of the test perform the

Question

y	x	xy	xx	yy
11.4	0	0	0	129.96
11.9	1	11.9	1	141.61
7.1	2	14.2	4	50.41
14.2	3	42.6	9	201.64
5.9	4	23.6	16	34.81
6.1	5	30.5	25	37.21
5.4	6	32.4	36	29.16
3.1	7	21.7	49	9.61
5.7	8	45.6	64	32.49
4.4	9	39.6	81	19.36
4	10	40	100	16
2.8	11	30.8	121	7.84
2.6	12	31.2	144	6.76
2.4	13	31.2	169	5.76
5.2	14	72.8	196	27.04
2	15	30	225	4
94.2	120	498.1	1240	753.66

SIMPLE LINEAR REGRESSION

Based on the table on the front of the test, perform the following tasks:                            

1. Graph and plot the 16 points (Use the blank graph on the next page of this test). 

1. Use the graph to estimate the Y intercept value                    Y Intercept = ___________

1. Use the graph to estimate Y if X = 3.5                                  Y Estimate = ___________ 

1. Calculate SS_xy (4 Points)

1. Calculate SS_xx (4 Points)

1. Calculate β₁       (4 Points)

1. Calculate β₀       (4 Points)

1. What is the Best Fit Line Equation for the 16 points based on Least Squares Linear Regression?   

9.  Use the Equation to estimate Y if X = 3.5                              Y Estimate = ___________

1.  What is the Correlation Coefficient and what does the value tell you about the correlation between X and Y?           

11.  What is the Coefficient of Determination and what does the value tell you about the correlation between X and Y?

12.  Based on your graph, does the data appear to be linear? - give comments to support your answer. (4 Points)

SIMPLE LINEAR REGRESSION

y	x	xy	xx	yy		Predicted Y	Residuals	Res. Squared
11.4	0	0	0	129.96		10.48456	0.915441	0.838032554
11.9	1	11.9	1	141.61		9.871559	2.028441	4.114573621
7.1	2	14.2	4	50.41		9.258559	-2.15856	4.659376179
14.2	3	42.6	9	201.64		8.645559	5.554441	30.85181682
5.9	4	23.6	16	34.81		8.032559	-2.13256	4.547807121
6.1	5	30.5	25	37.21		7.419559	-1.31956	1.741235479
5.4	6	32.4	36	29.16		6.806559	-1.40656	1.978407714
3.1	7	21.7	49	9.61		6.193559	-3.09356	9.570106173
5.7	8	45.6	64	32.49		5.580559	0.119441	0.014266195
4.4	9	39.6	81	19.36		4.967559	-0.56756	0.322123014
4	10	40	100	16		4.354559	-0.35456	0.125711957
2.8	11	30.8	121	7.84		3.741559	-0.94156	0.886533012
2.6	12	31.2	144	6.76		3.128559	-0.52856	0.279374426
2.4	13	31.2	169	5.76		2.515559	-0.11556	0.013353841
5.2	14	72.8	196	27.04		1.902559	3.297441	10.87311834
2	15	30	225	4		1.289559	0.710441	0.50472667
94.2	120	498.1	1240	753.66		94.19294	0.007059	71.32056311

13.  Use the table above to calculate the variance for the error squared values. (4 Points)            

14.  What are the upper and lower limits for estimating a 95% confidence interval test on the error squared values? (4 Points)

15.  What can you say about the best-fit estimating equation based on residual analysis? (4 Points)

 

1.      What are the three equations that would be solved simultaneously to get the 3 coefficients to make up the best-fit equation?

2.      The equation for this data model is    Y = - 5.48 + 0.014711 (b₁) + 2.8441 (b₂)

A current patient has a cholesterol level of 740, a BMI of 24.6, and his pulse is 88 bpm.  What would be his estimated pulse if he lowered his cholesterol to 200 and his BMI to 22?

3.      What is the Mean Square of the Errors?

4.      What is the standard deviation of the residuals?

5.      What is the 95% CI for the residuals?

6.      Perform the Residual Analysis.

7.      What is the Coefficient of Determination and what does the coefficient of determination tell you?

8.      What is the Calculated F value (for this model) to be used in an ANOVA test?

9.      What is the critical F value for the ANOVA Test?

10.   What is your conclusion of this test model based on the ANOVA test?