Question

Suppose a statistician built a multiple regression model for predicting the total number of runs scored by a baseball team during a season. Use the β estimates to predict the number of runs scored by a team with 337 ​walks, 820 ​singles, 224 doubles, 27 triples, and 108 home runs.		Ind. Var.	β estimate	Standard Error
		Intercept	3.17	14.06
		Walks x1	0.39	0.03
		Singles x2	0.41	0.05
		Doubles x3	0.65	0.04
		Triples x4	1.01	0.17
		Home Runs x5	1.52	0.04

The model predicts _________ runs for the season. ​(Round to the nearest whole number as​ needed.)

Answer 1

we know that multiple regression is given as

y =

Multiple regression based upon the given data table is

Number of runs = 3.17 + 0.39(walks) + 0.41(singles)+0.65(doubles)+1.01(triples)+1.52(home runs)

we have to find the total number of runs scored by a team with 337 ​walks, 820 ​singles, 224 doubles, 27 triples, and 108 home runs.

so, setting walks = 337, singles = 820, doubles = 224, triples = 27 and home runs = 108

we get the required total number of runs

Number of runs = 3.17 + 0.39(337) + 0.41(820)+0.65(224)+1.01(27)+1.52(108)

this gives

Number of runs = 3.17 + 131.43 + 336.2 + 145.6 + 27.27 + 164.16

or

Number of runs = 807.83

rounding to nearest whole number, we get 808

So, total number of runs scored by the team = 808 runs