An analyst was interested in the relationship between a company's assets and sales. She created the displayed regression analysis. She took the logarithm of these variables to make the relationship more linear. The assumptions for regression inference appeared to be satisfied. Use the output to the right to complete parts a and b. Dependent variable is: LogSales R squared = 34.8% s = 0.4462 with 82 – 2 = 80 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept 1.212 0.4955 2.45 0.0165 LogAssets 0.431 0.3685 1.17 0.2455 a) Is there a significant linear association between LogAssets and LogSales? Find the t-value and P-value to test an appropriate hypothesis and state your conclusion in context. First, state the appropriate hypotheses. H0: There is linear association between LogAssets and LogSales (?1 0). HA: There is linear association between LogAssets and LogSales (?1 0).
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The t-ratio is 1.17 and the P-value is 0.2455. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Show more…
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A regression model relating the number of salespersons at a branch office to the annual sales at the office (in thousands of dollars) provided the following regression output: ANOVA df SS MS F Significance F Regression 6 300.5 50.08 6.00 Residual 8 611.8 76.47 Total Coefficients Standard Error t Stat P-value Intercept 75.0 11.915 6.30 0.000 Number of Salespersons 60.0 5.592 10.74 0.000 a. Write the estimated regression equation (to the whole number). b. Compute the t statistic and test the significance of the relationship at a 0.05 level of significance (to 2 decimals). P-value is less than 0.01. We reject the null hypothesis. c. Compute the F statistic and test the significance of the relationship at a 0.05 level of significance (to 2 decimals). P-value is less than 0.01. We reject the null hypothesis. d. Predict the annual sales at the Memphis branch office. This branch employs 5 salespersons. $ 435 thousand (to the whole number)
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