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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99	52	234	61
105	38	263	67
88	25	212	71
76	48	126	69
79	47	150	60
56	23	236	70
60	22	174	71
121	57	219	69
61	20	137	65
108	29	263	72
97	33	231	59
77	50	109	66
59	54	140	63
78	41	180	62
63	41	141	64
63	20	116	71
72	24	113	69
95	39	240	72
91	51	122	67
93	34	244	62
81	38	112	74
72	31	118	64
93	47	254	66
69	58	141	67
55	34	203	59
62	24	101	63
55	28	165	67
75	52	157	63
60	33	184	63
91	38	212	60

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.

For partsc)andd), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables.

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_efor 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_e(to 3 decimal places) is:

increased decreased unchanged