Inference for regression

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. A regression on a random sample of 23 houses gives slope b. What does b estimate?
    1. The slope β₁ of the population regression line
    2. Nothing: b is the true slope
    3. The correlation r
  2. The residual plot of a regression on 85 points fans out: residuals spread more as x grows. Which condition fails?
    1. Equal variance of the residuals
    2. Linearity
    3. Normality of the population
  3. Computer output gives slope b = 8/10 with standard error SE_b = 3/100. Find the t statistic for H₀: β₁ = 0.
  4. A regression uses 41 data pairs. How many degrees of freedom does the t test for the slope have?
  5. In regression output, the row for x reads: Coef 0.97, SE Coef 0.08, and a t value. Which number is the slope's standard error?
    1. The SE Coef in the x row
    2. The Coef in the x row
    3. The value s (the SD of the residuals)
  6. With 30 pairs, b = 2/10 and SE_b = 7/100. Using t* = 2.048 (28 df, 95%), find the upper end of the interval for β₁.
  7. A 95% interval for the slope β₁ is (0.4, 0.8). What does it suggest?
    1. Convincing evidence of a positive linear relationship: 0 is not in the interval
    2. No evidence of a relationship
    3. x causes y to increase
  8. SE_b = 1/100 and t* = 2.048. Find the width of the 95% confidence interval for β₁.
  9. To test whether x is useful for predicting y (from 51 pairs), what is the null hypothesis?
    1. H₀: β₁ = 0, no linear relationship in the population
    2. H₀: b = 0
    3. H₀: r = 1
  10. An observational study tests H₀: β₁ = 0 for hours of sleep (x) and test score (y). The P-value is 0.006. What can you conclude?
    1. Convincing evidence of a linear association between sleep and scores in the population sampled
    2. More sleep causes higher scores
    3. The correlation must be close to 1
  11. Output shows slope b = 6/10 and t = 9 for H₀: β₁ = 0. Find SE_b.