What is the significance of the t stats and p values? SUMMARY OUTPUT Regression

Question

What is the significance of the t stats and p values?

SUMMARY OUTPUT Regression Statistics Multiple R 0.998689 R Square 0.99738 99.74% Adjusted R Square 0.992139 Standard Error 10.20215 Observations 7 ANOVA df SS MS F Significance F Regression 4 79238.14 19809.54 190.323 0.005234 Residual 2 208.1676 104.0838 Total 6 79446.31 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Intercept -2084.40 247.2367 -8.43081 0.013779 -3148.18 -1020.63 -3148.18 Toyota Price per Unit in US$ 0.03 0.010944 2.329483 0.145194 -0.02159 0.072581 -0.02159 Honda Price per Unit in US$ 0.085 0.019442 4.355129 0.048889 0.00102 0.168325 0.00102 Average Retail Gas Prices per gallon -137.133 8.617636 -15.913 0.003926 -174.211 -100.054 -174.211 Toyota Advertising in Billion U.S. dollars 134.8015 43.78853 3.078467 0.091299 -53.6053 323.2084 -53.6053

Explanation / Answer

Here it is F statistic that is shown in the table.

From this we calculate the p value which is interpreted as below:

A small p-value (typically 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

Here, since p value is very small we reject the null hypothesis.

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