Question

Following is a portion of the excel output for a regression analysis relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.

anova
df ss
regression 1 1575.76
residual 8 349.14
total 9 1924.90

coefficients standard error
intercept 6.1092 .9361
usage 0.8951 .149

What is the value of R-squared?
a. 0.18
b. 0.89
C. 0.05
d. 0.82

Answer 1

option d. 0.82, The value of R-squared for the regression analysis is calculated using the sums of squares provided in the Excel output, resulting in a coefficient of approximately 0.8185, or 81.85%, which corresponds to answer option d. 0.82.

Step-by-step explanation:

The value of R-squared in a regression analysis is calculated by dividing the sum of squares of the regression (SS Regression) by the total sum of squares (SS Total). The formula is R-squared = SS Regression / SS Total. From the provided Excel output, we have SS Regression = 1575.76 and SS Total = 1924.90. Using these values, we calculate R-squared as follows:

R-squared = SS Regression / SS Total

R-squared = 1575.76 / 1924.90

R-squared ≈ 0.8185

When expressed as a percentage, this value is approximately 81.85%, which means that around 81.85% of the variation in maintenance expense can be explained by the variation in usage hours.

Thus, the correct answer from the provided options is d. 0.82.