Question

a company want to find out if there is a linear relationship between indirect labor expense (ile), in dollars, and direct labor hours (dlh). data for direct labor hours and indirect labor expense for 25 months are given. approximately what percentage of the variation in indirect labor expenses is explained by the regression model you derived? place your answer, rounded to 2 decimal places, in the blank. do not use any stray punctuation marks or a percentage sign. for example, 78.91 would be a legitimate entry.
DLH(X) 20 25 22 23 20 19 24 28 26 29 22 26 ILE(Y) 361 355 376 384 374 311 427.2 387.5 450.8 475.2 462.6 333.3 389.9 445 511 501.1 544.9 423.8 574.1 535.4 444.7 578.4 399.6 355 313 25 28 32 33 34 30 36 37 31 20

Answer 1

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)/$\sqrt{VARX} . \sqrt{VARY}$

Coefficient of covariance (r) = 288.5216/$(\sqrt{30.9664} . \sqrt{5936.223})$

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.

To learn more about the variance visit: https://brainly.com/question/29365746

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