AP Statistics Inference for the Slope of a Regression Line Worksheet (PDF)

AP Statistics math worksheet: Inference for the Slope of a Regression Line – Maths PDF

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This inference slope worksheet for AP Statistics covers inference for the slope of a regression line (Common Core AP STAT 9.1, AP STAT 9.2, AP STAT 9.3, AP STAT 9.4, AP STAT 9.5, AP STAT 9.6, HSS-ID.B.6), with a free PDF to print.

These 20 problems practice AP Statistics topics 9.1 to 9.6. You will check LINER conditions, read computer output, build and interpret t intervals for a slope, test H0: beta = 0, and choose the correct inference procedure for a given situation.

AP Statistics · Common Core State Standards: AP STAT 9.1, AP STAT 9.2, AP STAT 9.3, AP STAT 9.4, AP STAT 9.5, AP STAT 9.6, HSS-ID.B.6

Inference slope worksheet: exercises 1 to 10

Exercise 1 – Parameters

Least-squares line: y-hat = 1.00 + 1.133x.

Using the scatterplot of practice hours and free throws made, define the true slope beta in context and write the hypotheses to test for a linear relationship.

Exercise 2 – LINER conditions

The LINER conditions for inference about a slope.

List what each letter in LINER stands for and tell how Equal variance is checked.

Exercise 3 – Residual plot

No pattern in the residuals and roughly constant spread: a linear model is appropriate.

Does the residual plot support the Linear and Equal variance conditions? Explain.

Exercise 4 – Read the output

Regression output: the Hours row gives the slope, its standard error, t, and the two-sided P.

From the computer output, state the regression equation and the standard error of the slope.

Exercise 5 – Interpret the slope

Interpret the slope 1.133 in the free-throw regression.

Exercise 6 – Degrees of freedom and t*

For a sample of 12 players, find df and the critical value t* for a 95% interval for the slope.

Exercise 7 – Confidence interval

95% interval for the true slope: (0.901, 1.365); 0 is not included.

Construct the 95% confidence interval for the true slope.

Exercise 8 – Interpret the interval

Interpret the interval (0.901, 1.365) in context.

Exercise 9 – t statistic

From the output, compute t for H0: beta = 0.

Exercise 10 – Conclusion

Two-sided p-value for the slope: 0.0000.

The output P value is 0.0000. State the conclusion at alpha = 0.05.

Exercises 11 and up

Exercise 11 – Interval and test

A 95% interval for the slope is (-0.4, 1.9). What is the conclusion of a two-sided test of H0: beta = 0 at alpha = 0.05?

Exercise 12 – Temperature and sales

Output for hot cocoa sales.

The output comes from a random sample of 10 days, predicting hot cocoa sales (cups) from the high temperature (degrees C). Test whether sales and temperature have a linear relationship at alpha = 0.05, and write the equation.

Exercise 13 – Interval from output

Using the hot cocoa output, find a 99% interval for the true slope.

Exercise 14 – R squared and r

The output shows R-Sq = 94.5%. Find r and interpret r squared.

Exercise 15 – One-sided test

A researcher believes more rainfall leads to more mud on a trail. The output for a sample of 15 days shows slope 0.62, SE 0.30, and a two-sided P value of 0.059. Test Ha: beta > 0 at alpha = 0.05.

Exercise 16 – Residual plot warning

A curved residual pattern.

The residual plot of a regression is shown. Is a t procedure for the slope appropriate?

Exercise 17 – Choose a procedure

Choosing a procedure.

Name the best procedure: (a) estimate the change in average salary per year of experience from a random sample of 40 workers; (b) test whether the proportion of defective items differs between two machines; (c) test whether a die is fair.

Exercise 18 – Standard error of the slope

For a regression with s = 2.4 (standard deviation of residuals), n = 20, and s_x = 3, find the standard error of the slope.

Exercise 19 – Multi-step

A random sample of 18 used cars gives slope -1.35 (thousand dollars per year of age) and SE_b = 0.21. Test H0: beta = 0 and give a 95% interval for the slope.

Exercise 20 – Predict and caution

Least-squares line: y-hat = 1.00 + 1.133x.

Using y-hat = 1.00 + 1.133x for the free-throw data (x between 2 and 13 hours), predict y at x = 8 and explain why x = 40 should not be used.

Key facts behind this inference slope worksheet

Key facts

Parameter: true slope beta; statistic: sample slope b; df = n – 2.
Interval: b +/- t* SE_b; test: t = (b – 0)/SE_b for H0: beta = 0.
LINER: Linear, Independent, Normal residuals, Equal variance, Random.
Computer output gives b, SE_b, t, and the two-sided P in the row for the explanatory variable.
If the interval contains 0, there is no convincing evidence of a linear relationship.

How to use this inference slope worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the inference slope worksheet as a PDF with the button below and keep it with your notes.

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