ISYE 6414 OFFICIAL MIDTERM 1 ACTUAL
EXAM PAPER 2026 QUESTIONS WITH
ANSWERS GRADED A+
◍ A dataset contains 696 data points and 10 categories with:SSTR = 1250SSE
= 3750Select the correct value of F₀. (Make sure to check the last two
decimal places)27.722.8625.40 None of the above.
Answer: 25.40
◍ Testing hypotheses.
Answer: of association relationships
◍ j.
Answer: is the index within group
◍ A multiple linear regression model was used to estimate the response
variable Y using the predictors X1, X2, X3 (see picture)What is the total
number of observations used for building this MLR model?17941797
17991800.
Answer: 1800 Explanation (from Module 3 Topic 3.2 Lesson 6):The
residual degrees of freedom n−p−1=1794Number of predictors,
p=5Solving:n = 1794+ 5 + 1 =1800
◍ If there's no pattern in this plot,.
Answer: we conclude the linearity assumptionholds.
◍ The first column in the ANOVA table.
Answer: are the degrees of freedom for each source ofvariability
◍ For a significance level of α=0.05\alpha = 0.05α=0.05, we found that the
predicting variable X1*X2 is statistically significant. What is the possible
p-value of this predictor?p=0.05p<0.05p>0.05Both Options 1 & 2.
, Answer: Both Options 1 & 2 A variable is considered statistically significant
if:p≤0.05This includes both:p=0.05p<0.05So, both options 1 and 2 are valid
possibilities.
◍ Statistical significance means.
Answer: that ß1 is statistically different from zero.
◍ A standardized residual value greater than 1 is indicative of
multicollinearity. (T/F).
Answer: False(False, we check the values of standardized residuals to screen
for outliers, not for multicollinearity)
◍ matrix form.
Answer: In multiple linear regression, the model can be written in ____
◍ In simple linear regression, we have the following assumptions about the
error terms: Select ALL correct answers.Mean of error terms is 0. Constant
Variance Independent random variable Chi-Square distributed with n–2
degrees of freedom.
Answer: Mean of error terms is 0. Constant Variance Independent random
variable (In simple linear regression, we assume the error terms have a zero
mean, constant variance, and are independent. A chi-square distribution is
not an assumption about the error terms themselves.)
◍ Y bar in ANOVA.
Answer: the meanestimate is the sample mean
◍ ß0 hat.
Answer: is the estimated expected value of the response variable, when
thepredicting variable equals zero
◍ SSE.
Answer: is the sum of square differences between the observations and the
individual sample means
◍ MSST.
Answer: SST/k-1 = between-group variability
, ◍ In ANOVA with k population samples, the sampling distribution of the
pooled variance is a chi-square distribution with N - 2 degrees of freedom.
(T/F).
Answer: False (False, the sampling distribution of the pooled variance is a
chi-square distribution with N - k degrees of freedom.)
◍ How can we use statistical inference based on hypothesis testing to test for
statistical significance of individual ßj?.
Answer: Using t-test. If this t-value is large, we reject the null hypothesis
and conclude that the coefficient is statistically significant
◍ we use ß1 hat.
Answer: when we interpret whether the relationship between x and y is
positive, negative, orthere is no relationship.
◍ Given a simple linear regression model, for a future value y (at x), the
prediction interval is narrower than the confidence interval for the mean
response. (T/F).
Answer: False(False, the line estimate is the same, but the interval is wider
than the confidence interval for the mean response)
◍ First Order Interaction model.
Answer: the contours of the regression function are non-parallel straight
lines for any interaction model. Here, when x1 is increased by 1, the
expected change in Y is β1 plus β3 times x2 thus depending on x2.
◍ Both the true errors and the model residuals in multiple linear regression
have constant variance. (T/F).
Answer: False(False. While the true errors have constant variance, the
estimated residuals do not)
◍ If that T value is large.
Answer: reject the null hypothesis that ß1 is equal to zero. Ifthe null
hypothesis is rejected, we interpret this that ß1 is statistically significant.
◍ ANOVA can be used to compare medians across more than two groups.
EXAM PAPER 2026 QUESTIONS WITH
ANSWERS GRADED A+
◍ A dataset contains 696 data points and 10 categories with:SSTR = 1250SSE
= 3750Select the correct value of F₀. (Make sure to check the last two
decimal places)27.722.8625.40 None of the above.
Answer: 25.40
◍ Testing hypotheses.
Answer: of association relationships
◍ j.
Answer: is the index within group
◍ A multiple linear regression model was used to estimate the response
variable Y using the predictors X1, X2, X3 (see picture)What is the total
number of observations used for building this MLR model?17941797
17991800.
Answer: 1800 Explanation (from Module 3 Topic 3.2 Lesson 6):The
residual degrees of freedom n−p−1=1794Number of predictors,
p=5Solving:n = 1794+ 5 + 1 =1800
◍ If there's no pattern in this plot,.
Answer: we conclude the linearity assumptionholds.
◍ The first column in the ANOVA table.
Answer: are the degrees of freedom for each source ofvariability
◍ For a significance level of α=0.05\alpha = 0.05α=0.05, we found that the
predicting variable X1*X2 is statistically significant. What is the possible
p-value of this predictor?p=0.05p<0.05p>0.05Both Options 1 & 2.
, Answer: Both Options 1 & 2 A variable is considered statistically significant
if:p≤0.05This includes both:p=0.05p<0.05So, both options 1 and 2 are valid
possibilities.
◍ Statistical significance means.
Answer: that ß1 is statistically different from zero.
◍ A standardized residual value greater than 1 is indicative of
multicollinearity. (T/F).
Answer: False(False, we check the values of standardized residuals to screen
for outliers, not for multicollinearity)
◍ matrix form.
Answer: In multiple linear regression, the model can be written in ____
◍ In simple linear regression, we have the following assumptions about the
error terms: Select ALL correct answers.Mean of error terms is 0. Constant
Variance Independent random variable Chi-Square distributed with n–2
degrees of freedom.
Answer: Mean of error terms is 0. Constant Variance Independent random
variable (In simple linear regression, we assume the error terms have a zero
mean, constant variance, and are independent. A chi-square distribution is
not an assumption about the error terms themselves.)
◍ Y bar in ANOVA.
Answer: the meanestimate is the sample mean
◍ ß0 hat.
Answer: is the estimated expected value of the response variable, when
thepredicting variable equals zero
◍ SSE.
Answer: is the sum of square differences between the observations and the
individual sample means
◍ MSST.
Answer: SST/k-1 = between-group variability
, ◍ In ANOVA with k population samples, the sampling distribution of the
pooled variance is a chi-square distribution with N - 2 degrees of freedom.
(T/F).
Answer: False (False, the sampling distribution of the pooled variance is a
chi-square distribution with N - k degrees of freedom.)
◍ How can we use statistical inference based on hypothesis testing to test for
statistical significance of individual ßj?.
Answer: Using t-test. If this t-value is large, we reject the null hypothesis
and conclude that the coefficient is statistically significant
◍ we use ß1 hat.
Answer: when we interpret whether the relationship between x and y is
positive, negative, orthere is no relationship.
◍ Given a simple linear regression model, for a future value y (at x), the
prediction interval is narrower than the confidence interval for the mean
response. (T/F).
Answer: False(False, the line estimate is the same, but the interval is wider
than the confidence interval for the mean response)
◍ First Order Interaction model.
Answer: the contours of the regression function are non-parallel straight
lines for any interaction model. Here, when x1 is increased by 1, the
expected change in Y is β1 plus β3 times x2 thus depending on x2.
◍ Both the true errors and the model residuals in multiple linear regression
have constant variance. (T/F).
Answer: False(False. While the true errors have constant variance, the
estimated residuals do not)
◍ If that T value is large.
Answer: reject the null hypothesis that ß1 is equal to zero. Ifthe null
hypothesis is rejected, we interpret this that ß1 is statistically significant.
◍ ANOVA can be used to compare medians across more than two groups.
