Practice Inference for Regression in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Using hypothesis tests and confidence intervals to draw conclusions about the true population slope \beta_1 of the linear relationship y = \beta_0 + \beta_1 x + \varepsilon, based on sample data.
You computed a sample regression line with slope b = 2.3. But is the true population slope actually different from zero? Maybe there's really no linear relationship and you just got a slope by chance. The regression t-test asks: 'Is my sample slope far enough from zero that it's unlikely to have occurred by random variation alone?'
Example 1
mediumA regression output shows: slope b=2.5, SE_b=0.8, n=30. Test H_0: \beta=0 vs H_a: \beta \neq 0 at \alpha=0.05 using a t-test.
Example 2
hardConstruct a 95% confidence interval for the slope \beta given: b=1.8, SE_b=0.5, n=25, and t^*_{0.025,23}=2.069.
Example 3
easyList the four conditions for valid regression inference and explain why each must be checked.
Example 4
hardA regression of salary on years of experience gives: \hat{y} = 30000 + 2000x, R^2=0.72, slope p-value=0.001. A confidence interval for the slope is (1500, 2500). Provide a full interpretation of each result.