The exercise involving data in this and subsequent sections

The exercise involving data in this and subsequent sections were designed to be solved using Excel The exercise involving data in this and subsequent sections were designed to be solved using Excel. The following estimated regression equation is based on 10 observations: ■ = 29.1270 + 0.5906 x 1 + 0.4980 x 2 Given data include: SST = 6724.125, SSR = 6216.375, S b1 = 0.0813, and S b2 = 0.0567.

Paper For Above instruction This analysis aims to evaluate the significance of regression coefficients in a multiple linear regression model using statistical tests such as F-tests and t-tests, with data processed via Excel. The regression model predicts a dependent variable based on two independent variables, with specified regression coefficients, sum of squares, and standard errors. The core objective involves calculating mean squares, conducting hypothesis tests, and interpreting the statistical results to determine the significance of predictors.

Calculation of MSR and MSE The mean square regression (MSR) and mean square error (MSE) are essential for understanding the variation explained by the model versus the residual error. MSR is computed as SSR divided by the degrees of freedom for regression, which in a model with two predictors is 2 (number of predictors). MSE is calculated as SSE divided by the residual degrees of freedom, which is total observations minus the number of predictors minus 1 (n – k – 1).

Given that the total number of observations, n, is 10 and the number of predictors, k, is 2, the degrees of

freedom for regression (df regression) = 2, and for residual error (df residual) = 10 – 2 – 1 = 7.

MSR = SSR / df regression = 6216.375 / 2 = 3108.188 MSE = SSE / df residual. To find SSE, we subtract SSR from SST: SSE = SST – SSR = 6724.125 – 6216.375 = 507.75. Therefore, MSE = 507.75 / 7 ≈ 72.536.

Calculation of F-statistic and test interpretation The F-statistic is calculated as MSR divided by MSE: F = MSR / MSE = 3108.188 / 72.536 ≈ 42.88.

Using an F-distribution table or Excel to find the critical value at α = 0.05 with df1=2 and df2=7, the critical F-value is approximately 4.74. Since the calculated F (42.88) exceeds this critical value, we reject the null hypothesis that the regression model is not significant. t-tests for significance of regression coefficients For β 1 , the t-test statistic is computed as the estimated coefficient divided by its standard error: t = b 1 /S b1 = 0.5906 / 0.0813 ≈ 7.26.

The corresponding p-value is very small, less than 0.01, indicating strong evidence that β 1 is statistically significant at α = 0.05.

Similarly, for β 2 , t = 0.4980 / 0.0567 ≈ 8.78.

This t-value also results in a p-value less than 0.01, demonstrating that β

2 is statistically significant at the 0.05 level.

Conclusions Given the calculated F-statistic surpasses the critical value, the overall regression model is statistically significant. The t-tests further confirm that both independent variables significantly contribute to explaining the variation in the dependent variable. Therefore, the model provides a meaningful fit to the data, and individual predictors are influential.

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