The PulseRates data set has pulse, height and weight for 90 patients who had an

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

Explanation / Answer

(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

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