Correlation Coefficient = ∑(Xi¿− ́x)(Yi− ́y)√∑(xi− ́x)2∑(yi− ́y)2¿= RCoefficient of Determination= R2T statistic =^βiS.E.(βi)Table 1: Table showing Regression Parameters and their properties of Google sales vs YearHere, Multiple correlation coefficient R=0.37281R(square) or Coefficient of Determination= 0.13899Adjusted R square=0.12243 Standard Error=10.3925The Anova Table:DfSum of SquaresMean Sum ofSquaresF statisticSignificnce FRegression1906.5867925906.598.394060.005497292Residual525616.172467108--Total536522.759259---Table 2: Table showing Anova table associated with the regression of Google sales vs YearInterpretation of Correlation Coefficient:Here, the correlation coefficient is given as 0.37281. Hence there is a positive trend in the data astime increases the goggle sales will increase. It implies the company is running in profits. Interpretation of standard Error:Here in the regression output we get the standard error which is associated with the regression problem. This can be used to evaluate the accuracy of the forecasts. Standard error is used mainly to compute the accuracy of the forecasts as with the help of it we can get the limit in which the 95% of the values should lie . It gives the interpretation that they should lie inside ±2*Standard Error of the regression. In this way we can quickly deduce an estimate of the prediction interval precisely 95%. As the standard error is 10.3925 so the prediction interval will be ±2*10.3925 From the above table we get the coefficients of intercept and t variable. P values associated with them is less than 0.05(significance level) which implies the regression is significant. Interpretation of the confidence intervals of the coefficients of “t” and intercept: As the confidence interval of intercept is (6.64,17.83) i.e. it does not contain 0 so it is significant. On the other hand confidence interval of coefficient of “t” is (0.0808,0.445) so it does not contain 0 hence it is also significant. Adjusted R square take into account the number of predictors. It penalizes for adding number of predictors.

STA 510 Business Statistics - Assignment

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