T Statistic

#1
I have been asked to complete a t test to determine if my coefficient and related variables are reliable enough. The variables are related to natural gas prices, one being the market price and the second being the price I receive. When I plot the points on a graph they seem to create a tight regression line. When I attempt to analyze the results in excel the answers seem skewed. How do I attempt to answer the t test question?
 

JohnM

TS Contributor
#2
The t-test you ran on the second tab in the Excel file is just a comparison between the means of the market price and the actual price. You won't get a significant result here since the means are pretty close and there is a lot of variation within each price column.

The t-test you should be interested in is the one on your "Regression" tab, which shows that the model coefficient of 1.2576 is reliable (significantly different from 0, which would suggest an unreliable coefficient).
 
#3
degree of freedom

Is it true that we always need to display degree of freedom with Chi-square and t-tests results? Do we need also need to display p-values? Thanks,
 
#4
Thanks for your help. One final question then. Is the "coefficients" value the same as the correlation coefficient? What does the "T Stat" amount of 30.88841731 represent? I'm very glad to hear that I can rely on the market price to determine my price...it might have been ugly if not!
 

JohnM

TS Contributor
#5
It's definitely helpful to display:

1. the calculated statistic and its p-value
2. the critical value of the statistic along with the associated degrees of freedom

It just shows that you were diligent in determining statistical significance.
 

JohnM

TS Contributor
#6
Completely Confused said:
Thanks for your help. One final question then. Is the "coefficients" value the same as the correlation coefficient? What does the "T Stat" amount of 30.88841731 represent? I'm very glad to hear that I can rely on the market price to determine my price...it might have been ugly if not!
No. The "coefficients" value is the slope of the regression "best fit" line and represents what you multiply the x-value by in order to get the y-value (predicted value).

In linear regression, the equation of the line follows y = bx + a, where b is the slope (coefficient) and a is the y-intercept.

The correlation coefficient "r" is an index of the strength of the relationship between the two variables, and can range between -1 (strong negative relationship) and 1 (strong positive relationship). 0 indicates no relationship.
 
#7
Ok, now I'm confused again. I'm supposed to be calculating the t statistics test for the regression coefficients instead of relying soley on R-squared. Is that what I'm doing? Once I calculate a number I'm supposed to compare that to a chart. What number am I looking for?
 

JohnM

TS Contributor
#8
Ok, now I'm confused again. I'm supposed to be calculating the t statistics test for the regression coefficients instead of relying soley on R-squared. Is that what I'm doing?

Yes.


Once I calculate a number I'm supposed to compare that to a chart. What number am I looking for?

In the Excel file, just look at the "t Stat" and "P value" - if the "P Value" is less than or equal to .05, then you can say that the coefficient is reliably larger than 0 at a 95% confidence level.