Question

A multiple regression model for predicting total number of runs scored by a Major League Baseball team during a season. Using data on all teams over a 9-year period (a sample of n=234), the results in the following table were obtained.

Independent Variable	Beta estimate	Standard Error	t
Constant	3.70	15.00	0.25
Walks (x1)	0.34	0.02	????
Singles (x2)	0.49	0.03	16.33
Doubles (x3)	0.72	0.05	14.40
Triples (x4)	????	0.19	6.00
Home runs (x5)	1.51	0.05	30.20
Stolen bases (x6)	0.26	0.05	5.20
Caught stealing (x7)	-0.14	0.08	-1.75
Strikeouts (x8)	-0.10	0.01	-10.00
Outs (x9)	0.10	0.01	10.00

Answer the following rounding off your answers to two decimal digits.

The T-test for significance of x1 is equal to ___________

Beta4 is equal to ______ The rejection region to test the significance of individual predictors at alpha 0.05 is equal

to ______ , therefore (use 1.00 = IS and 2.00 = ISN'T):

x2 _____ a good predictor at alpha 0.05

Moreover,

x3 _____ a good predictor at alpha 0.001

x8 _______ a good predictor at alpha 0.005

x7 is a good predictor at alpha ______

Answer 1

The T-test for significance of x1 is equal to

t-test statistic =    t = estimated slope / std error =   0.34   /   0.02   =   17.000

Beta4 is equal to

estimated slope= std error * t = 0.19 * 6 =   11.4

The rejection region to test the significance of individual predictors at alpha 0.05 is equal

critical t-value =    2.3646   [excel function: =t.inv.2t(α,df) ]               

| t-statistic | > | t critical value| MEANS GOOD PREDICTOR

x2 ___IS__ a good predictor at alpha 0.05

Moreover,

x3 _____IS__ ___ a good predictor at alpha 0.001

x8 ______IS__ ____ a good predictor at alpha 0.005

x7 is a good predictor at alpha __0.15____

Please revert back in case of any doubt.

Please upvote. Thanks in advance.