MGSC 291 Exam 3 Questions and Answers Latest Update

MGSC 291 Exam 3 Questions and Answers Latest Update 2025-2026

significant relationship - Answers if you reject Ho: β = 0, you are concluding there is a
____________ between X and Y

fit<-lm(quantitative response~predictor1+predictor2) - Answers R code for multiple regression

more than 1 predictor - Answers multiple regression is used when we have __________



equation:

Y = β0 + β1X1 + β2X2 + . . . + βkXk + ɛ



μY = β0 + β1X1 + β2X2 + . . . + βkXk

predict(fit,newdata=data.frame(predictor1=a,predictor2=b)) - Answers R code to predict mean Y
for a given set of x values

-if predictor is qualitative, must be in quotes



(predictor1=a, predictor2=b)

predict(fit,newdata=data.frame(predictor1=a,predictor2=b,interval="prediction", level=.9)) -
Answers R code for prediction interval

- for confidence interval, change "prediction" to "confidence"



(predictor1=a, predictor2=b, 90%)

residual - Answers ______ = y - ŷ

standard error - Answers the standard deviation for the residuals



referred to as:

- SY|X

- se

- Root MSE

,on average - Answers interpret the standard error of the regression:

predictions of (quantitative response) based on this model tend to be off by . . . ________

variability - Answers interpret R^2:

. . . % of the _______ in (quantitative response) is explained using (predictors) in this regression

adjusted R^2 - Answers R^2 almost always increases when additional predictor variables are
added (never decreases), so ________ should be used to decide if a new variable should be
added to the model

- imposes a "penalty" on each new term added to the model in order to make models w/
differing # of predictors more comparable

- ________ value might go down when a weak predictor is added to the model

- a larger gap when comparing R^2 to ________ suggests weak predictors are present in the
model

larger - Answers R^2 is ______ for multiple regression than for simple regression

at least 1 - Answers overall F test in multiple regression:



Ho: all regression coefficients are 0

HA: ________ predictor is important



interpret:

there is . . . evidence that ________ of the predictors in this model is important

R^2=0 - Answers the F test is equivalent to testing Ho: ________

P values - Answers the _________ for the individual predictors allow us to conclude whether that
predictor is important, after accounting for the other predictors in the model



(T tests)

<.001 - Answers overwhelming evidence for HA

P ______

, <.01 - Answers strong evidence for HA

P ______

<.05 - Answers sufficient evidence for HA

P ______

<.1 - Answers marginal evidence for HA

P ______

>.1 - Answers little to no evidence for HA

P ______

P value - Answers the probability, given that the null hypothesis is true, of observing a test
statistic that extreme or more extreme in the direction of the alternative hypothesis

- quantifies how extreme our test statistic would be, given that the null hypothesis is true

- this is evidence against the null hypothesis

T - Answers interpret individual ____ tests for predictors:



conclusion for hypothesis test:

. . . evidence to conclude (quantitative response) changes as (predictor) increases, after
accounting for (other predictor)



confidence interval:

w/ 95% confidence, after accounting for (other predictor), we expect (quantitative response) to
increase by . . . to . . . for each additional unit of (predictor)

after accounting for - Answers interpret the coefficient for a quantitative predictor:

________ (other predictor), we expect (quantitative response) to increase/decrease by . . . for
each additional unit of (predictor)

constant - Answers when interpreting coefficients, they assume the other variables are held
_______

- and multicollinearity means that might NOT be possible