I will be interpreting the first sample of the sales based on the rate of territories. Based on the given information, the number of rates is the independent variable, Y, and the number of revenue of sales is the treatment variable, or the dependent variable of X. The regression model, , is in this case y = 425.1x + 6573. This means the Y-intercept is 425.1 and the slope is 6573.
The least square estimate of the slope is 425.1 and the intercept is at 6573. This means that for every change in the X variable, in which this case is the number of shares of a territory, the number of revenue is going to increase by 425.1 dollars.
The 95% confidence interval is from lower limit -178.2 to upper limit 3022.3 of the slope. The intercept lies within the limit. The P-value is 0.077, which means that the null hypothesis of Ho = b1 is not rejected. We can also us the critical value approach as a extra precaution in the determination of rejecting or not rejecting the null hypothesis by calculating the t-statistic.
In testing the overall test of the significance of the regression parameters we use the ANOVA table. The F-test statistic is 7.01 with a p-value of 0.014. Since the p-value is less then 0.05 we do reject the null hypothesis that the regression parameters are zero at the significant level 0.05. Concluding that the parameters X and Y are jointly statistically significant at the significance level 0.05 but does not conclude that a cause-and-effect relationship is present.
The goodness of fit can be described through the coefficient of determination (R2 ), and also the estimated standard error of the regression equation to see how well the model fits into the set of observations. The coefficient of determination is 0.55, or 55%, and the estimated standard error of regression is 2.2 which provides an unbiased estimate of the standard deviation.
The regression will be used to predict the sales forecast to see which territory