Explain this regression line (regression to predict Close (Closing Price) with n

Question

Explain this regression line (regression to predict Close (Closing Price) with non-linear trend with two inflection points.

SUMMARY OUTPUT Regression Statistics Multiple R 0.946813 R Square 0.896454 Adjusted R Square 0.896247 Standard Error 3.675339 Observations 1004 ANOVA df SS MS F Significance F Regression 2 117064.1 58532.04 4333.100495 0 Residual 1001 13521.63 13.50812 Total 1003 130585.7 : Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 24.61135 0.348672 70.58588 0 23.92713491 25.29556 23.92713 25.29556 Day 0.035784 0.001602 22.3324 5.77651E-90 0.032639703 0.038928 0.03264 0.038928 Days^2 1.46E-06 1.54E-06 0.947789 0.343465423 -1.56629E-06 4.49E-06 -1.6E-06 4.49E-06

Explanation / Answer

Here the regression results for the line are as follows:

Since the F value is more than the critical F value, so the regression equation is as per statistically significant as the p value is less than 0.05 also.

Also the correlation coefficient is 0.89 which suggest that about 89% of the variability is explained by the regression equation while the balance 11% is unexplained.

With regards to the individual coefficients for intercept and variables, the t statistics for intercept and Day is more than the critical value while the Day^2 is less than the critical value which is also corroborated by p value.

As per p value, the intercept and Day is significant and hence should be included in the equation while Days ^ 2 is not significant and hence should not be included.

As the coefficient of Day is 0.035, so for every 1 unit change in the Day variable, then the Y variable increases by 0.035.

Also for Day =0, the Y value = intercept = 24.61.

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