Question

a. Construct a scatterplot of the data and tell why a linear regression model is appropriate. (Include this graph in your report.)   b. Run the linear regression procedure on StatCrunch and include the output in your report. c. Give the regression equation using the correct notation. d. Give the Coefficient of Determination AND interpret it.   e. Check the assumptions of the model by constructing each of the following plots and commenting on what they suggest in terms of the assumptions. (Include these graphs in your report.) 1. Fitted line plot 2. QQ-Plot of the residuals 3. Predicted values vs residuals


f. Test to see if the ‘before reading’ is useful in predicting the ‘after reading’. (Use ? = 0.05.) g. Instruct StatCrunch to save the 95% confidence intervals for the mean response. BUT DO NOT INCLUDE THE TABLE IN YOUR PROJECT. IT’S VERY BIG.   h. Use the table you created in part g to give the 95% confidence interval for the average ‘after reading’, when the ‘before reading’ is 60 bpm. i. Test to see if the ‘before reading’ and the ‘after reading’ are positively linearly correlated. (Use ? = 0.05.)

NOTE: Opinions may differ on whether or not the assumptions are met. For the sake of instruction, assume you can continue with the linear regression model to complete the project.

Pulse Rate Before (bpm)	Pulse Rate After (bpm)
89	77
85	70
82	73
58	56
61	58
64	61
60	59
59	57
63	61
61	59
64	62
63	58
68	60
65	65
66	72
60	54
59	55
59	56
60	57
58	57
59	57
82	77
73	68
77	75
75	73
79	75
81	78
78	69
80	72
76	69
90	83
87	82
94	82
92	84
105	86
108	84
85	70
80	67
77	66
83	65
72	69
70	68
75	75
98	87
107	90
103	88
100	84
95	82
105	91
93	88
102	90
110	89
57	41
49	39
50	37
53	49
56	50
49	44
57	55
48	49
50	48
69	65
67	64
68	66
82	64
75	66
79	71
77	76
74	72
76	72
74	74
72	69
75	73
73	77
72	77
70	73
75	62
70	64
72	77
61	46
63	57
64	75
85	57
79	61
77	73
73	67
76	61
78	69
68	64
71	60
77	69
91	84
89	87
86	88
74	69
77	73
76	70
75	57
79	61
73	61
75	59
79	65
72	80
74	70
92	86
66	72
65	66
64	66
62	60
66	70
63	68

Answer 1

Answer using Excel:

a. Construct a scatterplot of the data and tell why a linear regression model is appropriate. (Include this graph in your report.)  

b. Run the linear regression procedure on StatCrunch and include the output in your report.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.858003
R Square	0.73617
Adjusted R Square	0.733749
Standard Error	6.102274
Observations	111
ANOVA
	df	SS	MS	F	Significance F
Regression	1	11325.64	11325.64	304.1442	2.57E-33
Residual	109	4058.914	37.23775
Total	110	15384.56
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	13.51595	3.180927	4.249059	4.54E-05	7.211453	19.82044	7.211453	19.82044
Pulse Rate Before (bpm)	0.733551	0.042062	17.43973	2.57E-33	0.650185	0.816917	0.650185	0.816917

c. Give the regression equation using the correct notation.

y = 0.733x + 13.51

d. Give the Coefficient of Determination AND interpret it.

R = Coefficient of Defermination = sqrt(R squared) =0.858.

Correlation is positive and strong.

Post remaining questions saperately. Hope thsi will be helpful. Thanks and God Bless You :)