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: Heart Rate (bpm) Age (yrs) Weight (lb) Height (in) 77 54 178 63 69 39 138 58 108 57 227 68 88 48 154 64 59 58 154 57 84 59 180 73 62 30 232 71 119 54 242 65 65 38 169 61 62 27 182 66 56 34 208 58 60 31 243 62 81 42 213 74 108 56 205 69 56 56 124 71 89 59 213 65 68 28 209 72 57 23 188 62 107 55 212 59 95 50 221 61 55 48 154 60 110 49 196 61 110 33 250 64 62 29 109 63 90 33 201 74 73 51 121 70 88 55 159 63 59 49 103 66 69 36 214 68 57 34 102 65 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 is or is 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 decreased unchanged
