Inference for slopes practice questions (AP Statistics)

Sample questions

Key terms

The definitions and formulas AP Statistics expects for inference for slopes, typeset as they appear on the paper.

Sampling distribution of the slope

Different samples give different fitted slopes $b$. Under the conditions, $b$ is approximately Normal, centered at the population slope $\beta$, with a standard error that computer output reports as "SE Coef".

Conditions for inference on the slope

Linear relationship (residual plot has no pattern), independent observations (10 percent condition), Normal residuals at each $x$ (no strong skew or outliers), equal variance of residuals across $x$, and random sampling or assignment.

t-interval for the slope

Point estimate $b$ plus or minus a $t$ critical value times the standard error of the slope, with $n - 2$ degrees of freedom.

$$b \pm t^*\,SE_b, \qquad \text{df} = n - 2$$

t-test for the slope

Usually tests $H_0: \beta = 0$ (no linear relationship). Computer output gives $t$ and a two-sided p-value; halve the p-value for a one-sided alternative.

$$t = \frac{b - \beta_0}{SE_b}$$

Reading regression output

The "Constant" row gives the intercept and the predictor row gives the slope, each with its standard error, $t$ and p-value. $S$ is the standard deviation of the residuals; $R$-Sq is $r^2$.

Standard deviation of the residuals

The typical size of a prediction error from the regression line, in the units of $y$.

$$s = \sqrt{\frac{\sum (y_i - \hat{y}_i)^2}{n - 2}}$$

Frequently asked questions

Other AP Statistics topics

• Exploring one-variable data
• Exploring two-variable data
• Collecting data
• Probability, random variables and distributions
• Sampling distributions
• Inference for proportions
• Inference for means
• Chi-square tests

All AP Statistics topics · AP Statistics exam guide · All free practice exams