Question

A multiple regression model is to be constructed to predict the heart rate in beats per minute (bpm) of a person based upon their age, weight and height.

Data has been collected on 30 randomly selected individuals:

Point,Heart rate,Age,Weight,Height
1,62,22,148,74
2,57,28,105,57
3,84,52,109,70
4,120,43,211,61
5,76,38,164,62
6,72,47,109,69
7,117,49,215,73
8,115,41,259,70
9,118,59,213,61
10,65,39,114,71
11,84,53,115,67
12,99,23,258,57
13,80,30,262,64
14,76,35,123,58
15,75,41,173,74
16,104,44,161,73
17,92,53,198,60
18,61,39,122,62
19,108,42,237,65
20,69,30,214,70
21,121,52,180,57
22,94,48,136,63
23,76,43,172,72
24,65,38,134,58
25,65,20,199,60
26,82,36,187,74
27,55,26,195,70
28,64,44,114,65
29,125,55,186,58
30,116,58,212,69

1 of 7 ID: MST.MR.CM.01.0010 (14 points) A multiple regression model is to be constructed to predict the heart rate in beats per minute (bpm) of a person based upon their age, weight and height. Data has been collected on 30 randomly selected individuals: show data a) Find the multiple regression equation using all three explanatory variables. Assume that X1 is age, X2 is weight and X3 is height. Give your answers to 3 decimal places. weight + height ŷ = age + rejected. b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis c) The explanatory variable that is most correlated with heart rate is: age weight height d) The explanatory variable that is least correlated with heart rate is: age weight O height e) The value of R2 for this model, to 3 decimal places, is equal to f) The value of s for this model, to 3 decimal places, is equal to g) Construct a new multiple regression model by removing the variable height. Give your answers to 3 decimal places. The new regression model equation is: Û = age + weight h) In the new model compared to the previous one, the value of R2 (to 3 decimal places) is: O increased decreased O unchanged i) In the new model compared to the previous one, the value of s (to 3 decimal places) is: O increased O decreased O unchanged

Answer 1

Ans a ) using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.880604
R Square	0.775464
Adjusted R Square	0.749555
Standard Error	11.17922
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	3	11222.02	3740.672	29.93137	1.37E-08
Residual	26	3249.35	124.975
Total	29	14471.37
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	11.38138	25.63305	0.444012	0.660708	-41.3081	64.07088
age	1.437706	0.194001	7.410816	7.2E-08	1.038931	1.836481
weight	0.280253	0.042901	6.532599	6.32E-07	0.19207	0.368437
height	-0.49606	0.348454	-1.42361	0.16645	-1.21232	0.220195

a )

y = 11.381 + 1.438 Age - 0.496height

b )the null hypothesis is rejected

c )age

d ) height

e) the value of R square is 0.755

f)tha value of s is 11.179

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.87061
R Square	0.757961
Adjusted R Square	0.740032
Standard Error	11.38978
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	2	10968.73	5484.367	42.27618	4.81E-09
Residual	27	3502.633	129.7271
Total	29	14471.37
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-21.1002	11.902	-1.77283	0.087541	-45.5211	3.320686
age	1.435361	0.197648	7.262211	8.23E-08	1.029821	1.840901
weight	0.280839	0.043707	6.425524	6.95E-07	0.19116	0.370518

g )

y = -21.100 + 1.435 Age + 0.281height

h )decreased

i)increased

y = 11.381 + 1.438 Age - 0.496height

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