I cant really interpret it for you, but here's what all the numbers mean in context:
Constant
Coefficient
- This is the y-intercept of the regression line. With 0 wins, this model predicts that there will be 10834 attendants.
The other 3 values for the constant can usually be ignored.
Wins
Coefficient
- This is the slope of the regression line. For every win, this model predicts that there will be an additional 235 attendants.
SE Coefficient
- This is the standard error of the slope. If the data were to be collected again, you would expect the slope to vary by about 119.
- This also means about 68% of samples should be between 235 ± 119, or between 116 and 354. The same would apply for 95% between 2 standard errors away, and 99.7% between 3 standard errors away.
T-value
- Quoting minitab's blog here, "The t-value measures the size of the difference relative to the variation in your sample data."
- This is equal to the coefficient divided by the standard error of the coefficient: [tex]\frac{235}{119} =1.98[/tex].
- This t-value is calculated only on this sample, and would differ on another sample from the same population.
- The t-value is also directly linked to the p-value below.
Before moving on, I'll use these hypothesis:
- H₀ slope = 0 (null hypothesis, there is no relationship between the variables)
- H₁ slope ≠ 0 (alternative hypothesis, there is a relationship)
P-value
- This is the probability of getting a t-value farther away from 0 than our t-value (1.98).
- The p-value can be calculated from the t-value and the degrees of freedom (number of samples) depending on if this is a one-tailed or two-tailed test.
- The p-value of 0.058 here is greater than the common alpha value of 0.05 (95%, below), so we cannot reject the null hypothesis, suggesting that there is no statistically significant relationship between wins and attendants. It's close though, and with a slightly lower confidence interval like 0.06 (94%), we can reject the null hypothesis and conclude that there is a statistically significant relationship.
Alpha value
- The alpha value is a threshold used to judge if the test value is statistically significant.
- An alpha value of 0.05 is the most common, and this is a 95% confidence level, meaning you are 95% confident that the test results are accurate.
Other things
S
- This is the standard deviation of the residuals. 68% would fall within 7377 away from the line, 95% would fall within 14754, etc
R²
- This is the proportion of the variance that can be explained by the predictor. r² = 12.29% means only 12.29% of the variation in attendance can be explained by the number of wins.
Adjusted R²
- This one doesn't make too much sense to me in this context. An adjusted r² typically looks at whether any additional predictor variables are contributing to the predictions, but there are no additional predictors here, just wins.
Conclusion
Based on all that information, I wouldn't say attendances are influenced by the number of wins. The high p-value, high standard error, and low r² all contribute to my conclusion. Especially looking at the p-value, assuming a common alpha value of 0.05, the relationship between wins and attendances is not statistically significant. It's likely that the positive slope is due to an unknown 3rd variable that influences both attendances and wins, like the popularity of the baseball team. A more popular baseball team is more likely to be skilled, and therefore, a more popular baseball team will get more wins. A more popular baseball team will also obviously have more attendees.
However, if all you have to do is just interpret the slope all on its own, then you could say that the positive slope of the regression line means more wins = more attendees.