WGU C207 DATA-DRIVEN DECISION MAKING OA PRACTICE
QUESTIONS, VERIFIED ANSWERS & RATIONALES 100%
CORRECT(Regression Analysis)
Question 1 (Multiple Choice)
An operations manager runs a simple linear regression model to predict weekly
equipment maintenance costs ($y$) based on total operating hours ($x$). The resulting
regression equation is $\hat{y} = 150 + 4.25x$. What is the predicted maintenance cost
for a week with 40 operating hours?
● A. $\$170.00$
● B. $\$320.00$
● C. $\$325.00$
● D. $\$6,600.00$
Correct Answer: C. $\$325.00$
Rationale: Substitute $x = 40$ into the regression equation: $\hat{y} = 150 + 4.25(40) =
150 + 170 = 325$. The predicted cost is $\$325.00$.
Question 2 (Multiple Choice)
In the simple linear regression equation $\hat{y} = b_0 + b_1x$, what does the slope
coefficient ($b_1$) explicitly represent?
● A. The predicted value of $y$ when $x$ is equal to zero.
● B. The estimated change in the dependent variable ($y$) for a one-unit increase
in the independent variable ($x$).
● C. The strength of the correlation between two nominal variables.
● D. The total sum of squared residuals in the model.
Correct Answer: B. The estimated change in the dependent variable ($y$) for a
one-unit increase in the independent variable ($x$).
Rationale: The slope ($b_1$) measures the rate of change—how much the dependent
variable ($\hat{y}$) is expected to increase or decrease on average for every single-unit
increase in the independent predictor variable ($x$).
Question 3 (Multiple Choice)
What does the $y$-intercept ($b_0$) represent in a simple linear regression model?
, ● A. The average value of the dependent variable ($y$) when the independent
variable ($x$) equals zero.
● B. The maximum possible value that $y$ can attain in the dataset.
● C. The standard error of the estimate.
● D. The point where the regression line crosses the horizontal threshold of
significance ($\alpha$).
Correct Answer: A. The average value of the dependent variable ($y$) when the
independent variable ($x$) equals zero.
Rationale: By definition, the $y$-intercept is the point where $x = 0$, representing the
baseline value of $\hat{y}$ when the predictor variable has a value of zero (provided
zero is within or near the range of observed data).
Question 4 (Multiple Choice)
An analyst calculates the coefficient of determination ($R^2$) for a regression model
predicting employee performance scores based on training hours, yielding a value of
$0.81$. How should this $R^2$ value be interpreted in a business report?
● A. Exactly $81\%$ of the employees received a passing performance score.
● B. Approximately $81\%$ of the total variation in employee performance scores
can be explained by the linear relationship with training hours.
● C. There is a strong negative correlation of $-0.81$ between the two variables.
● D. The probability of committing a Type I error is $0.81$.
Correct Answer: B. Approximately $81\%$ of the total variation in employee
performance scores can be explained by the linear relationship with training hours.
Rationale: The coefficient of determination ($R^2$) measures the proportion of
variance in the dependent variable ($y$) that is predictable from or explained by the
independent variable(s) ($x$). An $R^2$ of $0.81$ means $81\%$ of the variance is
explained.
Question 5 (Multiple Choice)
If the coefficient of determination ($R^2$) of a linear regression model is $0.64$, what is
the correlation coefficient ($r$), assuming a positive linear relationship between the two
variables?
● A. $r = 0.36$
● B. $r = 0.80$
● C. $r = -0.80$
● D. $r = 1.28$
QUESTIONS, VERIFIED ANSWERS & RATIONALES 100%
CORRECT(Regression Analysis)
Question 1 (Multiple Choice)
An operations manager runs a simple linear regression model to predict weekly
equipment maintenance costs ($y$) based on total operating hours ($x$). The resulting
regression equation is $\hat{y} = 150 + 4.25x$. What is the predicted maintenance cost
for a week with 40 operating hours?
● A. $\$170.00$
● B. $\$320.00$
● C. $\$325.00$
● D. $\$6,600.00$
Correct Answer: C. $\$325.00$
Rationale: Substitute $x = 40$ into the regression equation: $\hat{y} = 150 + 4.25(40) =
150 + 170 = 325$. The predicted cost is $\$325.00$.
Question 2 (Multiple Choice)
In the simple linear regression equation $\hat{y} = b_0 + b_1x$, what does the slope
coefficient ($b_1$) explicitly represent?
● A. The predicted value of $y$ when $x$ is equal to zero.
● B. The estimated change in the dependent variable ($y$) for a one-unit increase
in the independent variable ($x$).
● C. The strength of the correlation between two nominal variables.
● D. The total sum of squared residuals in the model.
Correct Answer: B. The estimated change in the dependent variable ($y$) for a
one-unit increase in the independent variable ($x$).
Rationale: The slope ($b_1$) measures the rate of change—how much the dependent
variable ($\hat{y}$) is expected to increase or decrease on average for every single-unit
increase in the independent predictor variable ($x$).
Question 3 (Multiple Choice)
What does the $y$-intercept ($b_0$) represent in a simple linear regression model?
, ● A. The average value of the dependent variable ($y$) when the independent
variable ($x$) equals zero.
● B. The maximum possible value that $y$ can attain in the dataset.
● C. The standard error of the estimate.
● D. The point where the regression line crosses the horizontal threshold of
significance ($\alpha$).
Correct Answer: A. The average value of the dependent variable ($y$) when the
independent variable ($x$) equals zero.
Rationale: By definition, the $y$-intercept is the point where $x = 0$, representing the
baseline value of $\hat{y}$ when the predictor variable has a value of zero (provided
zero is within or near the range of observed data).
Question 4 (Multiple Choice)
An analyst calculates the coefficient of determination ($R^2$) for a regression model
predicting employee performance scores based on training hours, yielding a value of
$0.81$. How should this $R^2$ value be interpreted in a business report?
● A. Exactly $81\%$ of the employees received a passing performance score.
● B. Approximately $81\%$ of the total variation in employee performance scores
can be explained by the linear relationship with training hours.
● C. There is a strong negative correlation of $-0.81$ between the two variables.
● D. The probability of committing a Type I error is $0.81$.
Correct Answer: B. Approximately $81\%$ of the total variation in employee
performance scores can be explained by the linear relationship with training hours.
Rationale: The coefficient of determination ($R^2$) measures the proportion of
variance in the dependent variable ($y$) that is predictable from or explained by the
independent variable(s) ($x$). An $R^2$ of $0.81$ means $81\%$ of the variance is
explained.
Question 5 (Multiple Choice)
If the coefficient of determination ($R^2$) of a linear regression model is $0.64$, what is
the correlation coefficient ($r$), assuming a positive linear relationship between the two
variables?
● A. $r = 0.36$
● B. $r = 0.80$
● C. $r = -0.80$
● D. $r = 1.28$
