TEST-13-review

# TEST-13-review - Review Linear Regression t-tests...

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Review Linear Regression t-tests Name_____________________________ Source:Devore Class period_____ For questions #1-3, complete the following. a) Make a scatterplot and check for any obvious outliers. b) Find the equation of the least squares regression line. c) Calculate r and r 2 and explain what they mean. d) sketch the residual plot and determine if a linear equation is appropriate e) Interpret the slope and y-intercept in the regression equation. f) Predict the y value for the given x value. g) Test at the specified significance level if β is different from zero. h) Find s b . i) Construct the specified confidence interval for β . 1. The accompanying data on fish survival and ammonia concentration is taken from the paper “Effects off Ammonia on Growth and Survival of Rainbow Trout in Intensive Static Water Culture” . Let x = ammonia exposure (mg/L) and y = percent survival. x 10 10 20 20 25 27 27 31 50 y 85 92 85 96 87 80 90 59 62 f) let x = 30 g) use α = .05 i) 95% confidence interval 2. The paper “Root Dentine Transparency: Age Determination of Human Teeth Using Computerized Densitometric Analysis” ( Amer. J. Phys. Anthr. (1991):25-30) reported on an investigation of methods for age determination based on tooth characteristics. With y=age (years) and x = percentage of root with transparent dentine. The accompanying data is for anterior teeth: x 15 19 31 39 41 44 47 48 55 65 y 23 52 65 55 32 60 78 59 61 60 f) let x = 25 g) use α = .02 i) 98% confidence interval 3. The heights (in inches) are listed for boys who were measured at 5 years of age and again at 18 years of age. Age 5 43 41 42 45 46 Age 18 68 66 66 70 71 f) let x = 44 inches g) use α = .05 i) 95% confidence interval 4.a) What does a correlation coefficient of 1 mean? of - 2 mean? of 0 mean? b) Describe what finding the least squares regression line means. 5. a)The equation of a least squares regression line is y ˆ = 2.4 + 3.7 x . What is the residual for the point (3, 12)? What does this tell us about the actual point? b) What is the actual y value for x = 5 if the residual is 1.9? 6. A study concerning the relationship between the average ozone level y (in parts per million) and the population of a city x (in millions) resulted in the following MINITAB output.

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Predictor Coef Stdev t-ratio P Constant 8.892 2.395 3.71 0.002 popn 16.650 1.910 8.72 0.000 s = 5.454 R-sq = 84.4% R-sq(adj) = 83.3% Analysis of Variance SOURCE DF SS MS F P Regression 1 2260.5 2260.5 76.00 0.000 Error 14 416.4 29.7 Total 15 2676.9 a) What is the equation of the least squares regression line? b) Estimate the mean ozone level for a city having population of 1 million people. c) Determine the proportion of the observed variation in ozone levels that can be attributed to the population of a city. d) What is the correlation coefficient? f) Is the regression equation useful in predicting the average ozone level using the population of the city? Support your answer.
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