AGEC 317 Midterm

In the linear equation y = β0 + β1 x, what does β1 represent?

The slope or marginal effect of x on y

What does β0 represent in the same equation?

The value of y when x = 0

What does the derivative of a function measure?

- The instantaneous rate of change of y with respect to x

- The limit as the change in X approaches 0

For TC = 30Q + Q^2, what is marginal cost (MC)?

MC = 30 + 2Q

If the second derivative is positive, the function has a:

Minimum

In statistics, what is a population?

the entire group of interest

A statistic refers to:

A value calculated from a sample.

What kind of data lists company stock prices from 2015-2024?

- Time-series data

- It tracks one variable across time

What is the risk of rejecting a true null hypothesis?

Type I error (α).

- It's a false alarm — finding a difference that isn't real.

Q10: What is the risk of failing to reject a false null hypothesis?

Type II error (β).

- You miss a real effect.

The power of a test equals:

1 − β.

- It's the chance of correctly rejecting a false null.

In a one-sample t-test, what does t measure?

How many standard errors the sample mean is from the hypothesized mean.

Which formula is used for a one-sample t-test?

t = (x(mean) - μ) / (s / sqrt(n))

If p < α, what decision is made?

Reject the null hypothesis

In a paired t-test, what is tested?

Whether the mean of the differences = 0

What assumption must hold for a chi-squared test?

All expected frequencies must be ≥ 5

What does the chi-squared statistic measure?

The total of squared differences between observed and expected counts, scaled by expected counts.

Degrees of freedom for a 2×3 chi-squared table are

(2−1)(3−1) = 2

When χ2 > critical value, we:

Reject H0.

For a two-proportion chi-squared test, the null states

The population proportions are equal

What does an F-test compare?

Two variances or overall model fit.

Formula for F statistic (basic form):

F = s1^2 / s2^2.

- Variance ratio; larger variance goes on top

Degrees of freedom for F test

df1 = n1 − 1, df2 = n2 − 1

In regression, the F-test checks:

If the model explains y better than an intercept-only model.

If F > critical or p < α, we:

Reject H0 → model is significant.

What is the main purpose of regression analysis?

To estimate how x affects y.

In the model y = β0 + β1 x + ε, what does ε represent?

The random error term.

OLS estimates are chosen to minimize:

The sum of squared errors (SSE).

What does R^2 measure?

The proportion of variation in y explained by the model

Adjusted R^2 accounts for:

Number of predictors.

When you add more independent variables, what always happens to R^2?

It increases or stays the same.

The null hypothesis for a t-test on a coefficient β is:

H0: β = 0.

Formula for t-statistic of a coefficient:

t = β_i / SE(β_i).

A high p-value (> α) means:

Fail to reject H0.

In a regression F-test, what is H0?

All slope coefficients = 0

What is the main assumption behind least squares?

Errors have mean zero and constant variance.

What does a residual represent?

Difference between actual and predicted y

If residuals have pattern (e.g., curve), it suggests:

Model is misspecified

What happens if expected frequency < 5 in χ^2?

Test results become unreliable.

In hypothesis testing, α = 0.05 means:

5% chance of Type I error.

What kind of test compares two means from independent samples?

Two-sample t-test.

What kind of test compares two means from the same sample before and after?

Paired t-test.

What does p-value mean?

Probability of getting a result as extreme as observed if H0 is true.

When does the F-distribution appear?

When comparing two sample variances.

Why is the F-statistic always positive?

Variances can't be negative.

What are degrees of freedom used for?

To find critical values in t, F, and χ^2 tables.

What type of data classifies individuals by favorite color?

Qualitative nominal.

What's the danger of spreadsheet modeling?

Human error can produce false results.

Which came first historically: Lotus 1-2-3 or Excel?

Lotus 1-2-3.

Why use Adjusted R^2 instead of R^2 alone?

It accounts for number of predictors and prevents overfitting.

What are the arguments of a and b of the round function?

A is the #, B is the # digits we are rounding by

What is the error term?

accounts for the variation in the dependent variable that the independent variables do not explain.

Why do the SSE vary between the lines?

because of the different y hats

Is a chi-squared test a one or two-tailed test?

two-tailed

Why will the t-stat for a chi-squared test always be nonnegative?

because it is squared

- does the p-value change as alpha level changes?

- does the p-value change as the degrees of freedom changes?

- does critical value change as the DOF changes?

- does CV change as t-stat changes?

- no

- yes

- yes

- no