Unit 4 Assessment | Mathematics Project

Practice, not certification. This is an ungraded assessment with no timer, identity requirement, server-side score collection, or claim of educational accreditation. For questions involving real studies, use the stated assumptions.

Question 1 · The aggregate result reverses

A success rate ranks treatment A higher within each severity group, but B higher overall. What is a possible explanation?

Always a calculation errorDifferent severity-group weights in the two treatmentsAll subgroup rates must be equalProof of the causal effect of treatment B

Question 2 · Interpret a fitted slope

For y-hat = 12+3x, the fitted difference between x=5 and x=6 is?

131218

Question 3 · Prediction mistake

The observed response is 17 and fitted response is 12. The residual equals?

−5512/1729

Question 4 · What R² is not

For ordinary least squares with an intercept, R²=.9 tells us what?

The model has a 90% probability of being truex causes 90% of yIn sample, the model reduces squared error by 90% relative to the mean-only model under the usual definitionEvery prediction is 90% accurate

Question 5 · A slope's estimated uncertainty

A simple OLS model with intercept has n=5. What are the residual degrees of freedom for a slope t statistic?

3456

Question 6 · One-way ANOVA

Three groups of three values have means 3,5,7 and grand mean 5. What is between-group SS?

6122448

Question 7 · Interpret the global F rejection

A properly conducted one-way ANOVA rejects equality of three population means. What follows?

Every pair must differAt least one population mean differs under the tested modelThe largest group caused the differenceThe groups are normally distributed with certainty

Question 8 · Logistic regression scale

In a logistic model, exp(beta1) represents what?

A probability differenceAn odds ratio per x unit under the modelThe coefficient's p-valueThe response variance

Question 9 · Association versus causation

A multivariable observational regression estimates an adjusted association. What else is required for a causal claim?

Nothing if p<.05Strong justified design and identification assumptions about confounding, selection and interventionA very large R²At least five graphs

Question 10 · Air-quality data audit

Historical R airquality has 153 rows, with 37 missing Ozone readings. How many observed ozone values?

37111116153

Question 11 · Compare different regressions

Why fit simple and multivariable airquality models on the same complete-case sample?

To make every coefficient identicalTo distinguish changed covariates from changed observation setsTo ensure causal identificationTo remove seasonality automatically

Question 12 · Reproducibility

Which report is most reproducible?

One p-value without a datasetA chart without unitsDocumented source, cleaning, code, software assumptions and complete resultsA screenshot of a spreadsheet

Question 13 · Capstone claim

Which conclusion is appropriate for a historical observational air-quality regression?

Increasing temperature causes a precisely identified change in ozoneOzone readings in observed complete cases were associated with recorded temperature conditional on included covariatesThe model proves all New York seasons behave alikeThe p-value establishes that there were no missing values