Answer :
For the data given above, the Coefficient of determination r² obtained using the Coefficient of determination calculator is 0.45; which means that (0.45 * 100%) about 45% of the variation in indirect labor expense is explained by the regression line while 55% is due to other factors.
For mean:
Mean of x = ∑xi/n = 689/25 = 27.56 (where n = 25)
V (X) = ∑(xi^2)/n - Mean of x^2
V (X) = 19763/25 - 27.56^2
V (X) = 790.52 - 759.5536
V (X) = 30.9664
Similarly, Mean of y = ∑yi/n = 10713.5/25 = 428.54
V (Y) = ∑(yi^2)/n - Mean of y^2
V (Y) = 4739568.87/25 - 428.54^2
V (Y) = 189582.7548 - 183646.5316
V (Y) = 5936.2232
Variance of x = 30.9664
Variance of y = 5936.223
Covariance(X, Y) = 1/n∑xy - mean of x. mean of y
Covariance(X, Y) = (1/25 x 302477.1) - (27.56 x 428.54)
Covariance(X, Y) = 12099.084 - 11810.5624
Covariance(X, Y) = 288.5216
Coefficient of covariance (r) = COV(X,Y)/[tex]\sqrt{VARX} . \sqrt{VARY}[/tex]
Coefficient of covariance (r) = 288.5216/[tex](\sqrt{30.9664} . \sqrt{5936.223})[/tex]
Coefficient of covariance (r) = 288.5216/ (5.564746176 x 77.04688832)
Coefficient of covariance (r) = 288.5216/ 428.7463771
Coefficient of covariance (r) = 0.672942363
Therefore,
r= 0.672942
r^2= 0.452851
From the excel sheet and the values given above by calculating, we can see that r = 0.67 which indicates a weak linear relationship between X and Y.
r^2=.45 which indicates that 45% of the variation in indirect labor expenses could be explained by the regression model.
The coefficient of determination, r² gives the proportion of explained variance due to the regression line.
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The percentage of variation in indirect labor expenses explained by the regression model is given by the coefficient of determination (R^2), which requires the calculation of a correlation coefficient and subsequent analysis using a regression equation. Without the complete data, exact percentages cannot be provided.
To determine the percentage of variation in indirect labor expenses explained by the regression model, we first need to calculate the coefficient of determination (R^2). The steps involved would include:
- Creating a scatter plot to visualize the data for direct labor hours (DLH) and indirect labor expenses (ILE).
- Assessing the plot to identify any potential linear relationship.
- Using the method of least squares to calculate the regression line equation of the form:
ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope. - Finding the correlation coefficient (r), and squaring it to get R^2, which represents the percentage of the variance in the dependent variable that is predictable from the independent variable.
However, without the actual numerical data for all 25 months provided in the question, it is not possible to calculate the exact percentage of variation. One would typically use statistical software or a calculator to find the correlation coefficient and the coefficient of determination (R^2) based on the provided data points.
