Help with Interpreting Regression Results

[stunner5000pt]

Homework Statement

Determine if the intercept term is relevant

Relevant Equations

No equations, only interpretation

Hello all, need your help with interpreting regression reuslts

The results are given below for hte regression that I ran in Excel

Here, the dependent variable Pc is -63.28 with a standard error of 15.86.

But is this different from zero? I see the t-stat here is -3.99, and the p-value is 0.000215. In absolute value terms t > p, and thus Pc is different from zero.

But is this correct - should we use the absolute value of the t-stat? Or should we reject Pc since -3.99 < p value?

Summary Output
Regression Statistics​
Multiple R	0.491468698​
R Square	0.241541481​
Adjusted R Square	0.226372311​
Standard Error	90.29795564​
Observations	52​
ANOVA​
​	df​	SS​	MS​	F​	Significance F​
Regression	1​	129833.1911​	129833.1911​	15.92318335​	0.000216​
Residual	50​	407686.0396​	8153.720793​
Total	51​	537519.2308​
​	Coefficients​	Standard Error​	t Stat​	P-value​	Lower 95%​	Upper 95%​	Lower 95.0%​	Upper 95.0%​
Intercept	2135.576773​	457.8577755​	4.6642798​	2.34319E-05​	1215.942​	3055.211​	1215.942​	3055.211​
Pc	-63.28227342​	15.85868325​	-3.990386366​	0.000215714​	-95.1354​	-31.4292​	-95.1354​	-31.4292​

 

[WWGD]

I am not sure what you mean by being relevant , but the intercept is contained in the interval (1215.942,3055.211) with 95% confidence, so there is good reason to believe it is not 0, if that is what you mean.

 

[statdad]

"In absolute value terms t > p, and thus Pc is different from zero."

You never compare a t-statistic (or the absolute value of a t-statistic, or ANY statistic) to a p-value. Very crudely stated, you make the decision to reject a null hypothesis if

* the test statistic is in some sense "big"
or
* the associated p-value is determined to be "small"

The rest of your question seems poorly worded.

* "Here, the dependent variable Pc is -63.28 with a standard error of 15.86." No, your dependent variable is not -63.28. From the output it appears that the SLOPE of your regression line is -63.28, The p-value would indicate that you can conclude it is "statistically significant". In the traditional (frequentist) hypothesis testing setting that information would mean you would conclude that "the population slope is non-zero". (Remember that you don't know the actual value of the population slope, since -63.28 is merely a point estimate.)
* The output shows the sample intercept is 2135.6 (approximately), and the p-value says you could conclude it is significant.REMEMBER that "significant" here means statistically significant, which essentially means that you're able to reject the null hypothesis that the true intercept is zero. Whether the intercept is significant in a practical setting -- that is, whether it tells you anything useful about the relationship between your y and Pc -- depends on whether Pc values are ever zero. If not (if they are restricted to be strictly positive or strictly negative) then the intercept doesn't provide any useful information about your relationship.