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: hide data

Heart Rate (bpm)	Age (yrs)	Weight (lb)	Height (in)
78	23	245	70
91	44	223	68
79	42	178	67
60	33	200	58
57	25	99	68
59	35	123	64
78	30	204	62
98	56	200	63
87	57	203	60
77	39	243	63
82	42	147	59
56	24	178	64
62	49	144	69
105	39	249	73
91	54	119	65
59	59	133	59
71	53	177	69
66	27	119	63
98	55	217	66
60	35	101	58
100	36	245	60
92	46	164	74
84	41	208	68
80	26	230	63
90	30	195	62
107	32	256	59
70	49	192	74
86	43	168	59
65	22	234	65
99	49	194	64

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.

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 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:

y^ =  + age + weight

h)In the new model compared to the previous one, the value of R² (to 3 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

Answer 1