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

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58	43	194	71
86	49	165	62
61	46	135	62
63	21	222	75
85	28	227	58
102	59	243	64
69	26	202	68
70	42	237	70
72	25	165	64
69	23	163	58
71	26	176	70
71	29	129	64
63	33	186	63
62	34	135	66
82	53	204	69
96	58	220	58
56	28	225	69
71	25	177	62
90	57	197	71
73	56	166	65
78	44	190	58
71	30	228	65
71	55	111	63
63	40	149	73
70	30	221	74
55	30	239	64
72	41	212	60
60	23	157	64
69	21	242	74
56	37	165	75

a)Find the multiple regression equation using all three explanatory variables. Assume that x₁is age, x₂is weight and x₃is height. Give your answers to 3 decimal places.

y^=+age +weight +height

b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis

isis not

rejected.

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 height

e)The value of R²for this model, to 2 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:

y^=+age +weight

h)In the new model compared to the previous one, the value of R²(to 2 decimal places) is:

increased decreased unchanged

i)In the new model compared to the previous one, the value of s (to 3 decimal places) is:

increased decreased unchanged