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Simple Regression Results Interpretation
Null and Alternative Hypotheses
The dependent variable (y) is injuries (severity of injuries) while the independent variable (x) is hours of training. The study seeks to determine whether the hours of training are a significant predictor of the severity of injuries in case one gets hurt playing football. The regression equation is:
Y = a + bx
Where Y is the dependent variable, x is the independent variable, a is the y-intercept and b is the slope of the line.
The null and alternative hypotheses are:
H0: b = 0 (x has no effect on y)
HA: b ? 0 (changes in y are due to changes in x)
Results of Simple Regression a
Interpretation
p value = 0.011
significance level (alpha) = 0.05
R2 =0.21 (21%)
b = -0.125
a = 6.8473
The regression line Y is given by:
Y = 6.8473 - 0.125x
There negative slope (-0.125) indicates an inverse relationship between hours of training and the severity of injury. More hours of training are associated with the lower severity of injury in case one gets hurt while playing. Increasing the hours of training by 1hour would reduce the severity of injury by 12.5 percent.
To check whether the relationship is significant, we compare the p-value to the 0.05 alpha value. The p-value is 0.011, which is less than the alpha value of .05 (p<0.05). Thus, the p-value is significant. We reject the null hypothesis and conclude that changes in the dependent variable (severity of injury) are due to changes in the independent variable (hours of training). The hours of training are a significant predictor of the severity of injury. However, the R squared value of 0.21 indicates that the relationship is fairly weak the hours of training only predicts 20 percent of changes in the dependent variable, implying that there are other variables not captured in the analysis that influence the severity of a players injury.
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