Question

The PulseRates data set has pulse, height and weight for 90 patients who had an echocardiogram test in one of the clinic in Ottawa in the month of September. (a)[2] Fit a L-S regression line using height to predict the pulse rate (pulse rate is called the response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient)

(b)[2] Fit a L-S regression line using weight to predict the pulse rate (response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient) .

(c)[2] Fit a L-S regression line using height to predict the weight (response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient) .

(d) What is the predicted value for weight for a patient whose height is 68.7 inches?[1] .

For 71.5 inches?[1] . For 83 inches ?[1] . Which of these seem to make sense?[1] . Can you predict the height if the weight is 156 lb

Pulse	Height	Weight
64	66	140
58	72	145
62	73.5	160
66	73	190
64	69	155
74	73	165
84	72	150
68	74	190
62	72	195
76	71	138
90	74	160
80	72	155
92	70	153
68	67	145
60	71	170
62	72	175
66	69	175
70	73	170
68	74	180
72	66	135
70	71	170
74	70	157
66	70	130
70	75	185
96	61	140
62	66	120
78	68	130
82	68	138
100	63	121
68	70	125
96	68	116
78	69	145
88	69	150
62	62.75	112
80	68	125
62	74	190
60	71	155
72	69	170
62	70	155
76	72	215
68	67	150
54	69	145
74	73	155
74	73	155
68	71	150
72	68	155
68	69.5	150
82	73	180
64	75	160
58	66	135
54	69	160
70	66	130
62	73	155
76	74	148
88	73.5	155
70	70	150
90	67	140
78	72	180
70	75	190
90	68	145
92	69	150
60	71.5	164
72	71	140
68	72	142
84	69	136
74	67	123
68	68	155
84	66	130
61	65.5	120
64	66	130
94	62	131
60	62	120
72	63	118
58	67	125
88	65	135
66	66	125
84	65	118
62	65	122
66	65	115
80	64	102
78	67	115
68	69	150
72	68	110
82	63	116
76	62	108
87	63	95
90	64	125
78	68	133
68	62	110
86	67	150

Answer 1

(a)[2] Fit a L-S regression line using height to predict the pulse rate (pulse rate is called the response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient)

Ans:

The equation of the L-S regression line is
Pulse = 18.69 -0.6624 Height

Predictor Coef SE Coef T P
Constant 118.69 21.3600 5.56 0.000
Height -0.6624 0.3100 -2.14 0.035

S = 10.5969 R-Sq = 4.9% R-Sq(adj) = 3.9%

The estimated p-value for height is 0.035. Hence, it makes sense to use this line because the Height has significant effect on pulse rate at 0.05 level of significance. The correlation coefficient value is  -0.222.

(b)[2] Fit a L-S regression line using weight to predict the pulse rate (response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient) .

Ans: The equation of the L-S regression line is

The regression equation is
Pulse = 86.475 - 0.0918 Weight

Predictor Coef SE Coef T P
Constant 86.4750 7.027 12.31 0.000
Weight -0.0918 0.0477 -1.93 0.057

S = 10.6463 R-Sq = 4.0% R-Sq(adj) = 3.0%

The estimated p-value for covariate weight is  0.057. Hence, it does not make sense to use this line because the Weight has insignificant effect on pulse rate at 0.05 level of significance. The correlation coefficient value is  -0.201.

(c)[2] Fit a L-S regression line using height to predict the weight (response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient) .

Ans: The equation of the L-S regression line is

Weight = - 204.52 + 5.0875 Height

Predictor Coef SE Coef T P
Constant -204.52 30.09 -6.80 0.000
Height 5.0875 0.4367 11.65 0.000

S = 14.9304 R-Sq = 60.7% R-Sq(adj) = 60.2%

The estimated p-value for covariate weight is  0.000. Hence, it makes sense to use this line because the Height has significant effect on Weight at 0.05 level of significance. The correlation coefficient value is 0.779.

(d) What is the predicted value for weight for a patient whose height is 68.7 inches?[1] .

For 71.5 inches?[1] . For 83 inches ?[1] . Which of these seem to make sense?[1] . Can you predict the height if the weight is 156 lb

Ans:

The predicted value for weight for a patient whose height is 68.7 inches

Weight = - 204.52 + 5.0875 *68.7=144.99 lb

The predicted value for weight for a patient whose height is 71.5 inches

Weight = - 204.52 + 5.0875 *71.5=159.23 lb

The predicted value for weight for a patient whose height is 83 inches

Weight = - 204.52 + 5.0875 *83=217.74 lb

All make sense.

For predicting the height if the weight is 156 lb required the equation of the L-S regression line, that is,

Height = 51.452 + 0.1192 Weight

Predictor Coef SE Coef T P
Constant 51.452 1.509 34.10 0.000
Weight 0.1192 0.0102 11.65 0.000

S = 2.28576 R-Sq = 60.7% R-Sq(adj) = 60.2%

The predicted height if the weight is 156 lb is

Height = 51.452 + 0.1192*156 = 70.0472