Question

A fishing group ran a regression in which a catch (CATCH) is a function of several variables including: Training (TRAIN), Experience (EXP), Age (AGE), ability to swim (SWIM=1, otherwise 0), good heath (HEALTH=1, otherwise 0) and boat ownership (BOAT)

Swimming and health are dummy variables

CATCH = 10.482 + 0.211*TRAIN + .392*EXP - 0.416*AGE + 4.82*SWIM + 2.833*HEALTH + 3.822*BOAT + e

T-statistic TRAIN: (0.88) EXP:(1.88) AGE:(-1.41) SWIM:(4.70) HEALTH:(3.42) BOAT:(2.42)

R-square= .910; adjusted R-square= .882; SEE= .723

Pearson’s correlation coefficient ‘r’ between a catch and some of the independent variables: TRAIN: 0.625 (p=.004); EXP: 0.539 (p=.022); AGE: 0.334 (p=.041).

Please show through calculation whether or not these variables account for a catch and if there's a need for other analysis

Answer 1

R^2 = 0.910

adjusted R^2 = 0.882

k = 6

1 - (1- R^2)(n-1)/(n-k-1) = adjusted R^2

1 - (1- 0.910) (n-1)/(n-7) = 0.882

n = 26

p-value = 0.000 <alpha

hence we reject the null hypothesis

we conclude that the model is signficant

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