Question

The following table consists of one student athlete's time (in minutes) to swim 2000 yards and the student's heart rate (beats per minute) after swimming on a random sample of 10 days. Swim Time Heart Rate 34.13 144 35.74 152 34.73 124 34.03 140 34.14 152 35.73 146 36.16 128 35.56 136 35.39 144 35.58 148 Which point from the data has the largest residual? (x, y) = 35.58,148 Incorrect: Your answer is incorrect. Explain what the residual means in context. Is this point an outlier? An influential point? Explain. (Round your answers to two decimal places.) The residual means that when the swim time is Incorrect: Your answer is incorrect. , the observed heart rate is about Incorrect: Your answer is incorrect. beats less than the predicted rate. When this point is removed, it has a Correct: Your answer is correct. effect on the regression line, so it Correct: Your answer is correct. influential. The point Correct: Your answer is correct. an outlier, because the residual is Correct: Your answer is correct. twice the standard deviation.

Answer 1

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.116070918
R Square	0.013472458
Adjusted R Square	-0.109843485
Standard Error	10.0337
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	10.99891475	10.99891475	0.109251551	0.74948803
Residual	8	805.4010852	100.6751357
Total	9	816.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	190.6315686	148.9801426	1.279577031	0.236553833	-152.917256	534.1803932
Swim time, X	-1.401849956	4.241189973	-0.330532224	0.74948803	-11.18205156	8.378351652

The least square regression line is:

y' = 190.63-1.40x

Slope is negative. So

That is for additional minute added to swim time heart rate is decreased by 0.87.

The y-intercept is: 171.75

That is if student does not swim his heart rate will be 171.75.

The r^2 is 0.0160

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Following table shows all residuals

Swim time, X	Heart rate, Y	y'=190.63-1.40x	Residual=y-y'
34.13	144	142.848	1.152
35.74	152	140.594	11.406
34.73	124	142.008	-18.008
34.03	140	142.988	-2.988
34.14	152	142.834	9.166
35.73	146	140.608	5.392
36.16	128	140.006	-12.006
35.56	136	140.846	-4.846
35.39	144	141.084	2.916
35.58	148	140.818	7.182

That is largest residual is for point (34.73, 124).

The residual mean that when the swim time is 34.73 minutes the observed heart rate is about 18.008 beats less than predicted rate.