CH14 exercises solutions

# CH14 exercises solutions - X X X X X X X X X X X X X X X X...

This preview shows pages 1–4. Sign up to view the full content.

X X X X X X X X X X X X X X X X X AP Statistics Solutions to Packet 14 X Inference for Regression Inference about the Model Predictions and Conditions X X X X X X X X X X X X X X

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 HW #32 1, 2, 6, 7 14.1 AN EXTINCT BEAST, I Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Here are the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five fossil specimens that preserve both bones: Femur: Humerus: 38 41 56 63 59 70 64 72 74 84 The strong linear relationship between the lengths of the two bones helped persuade scientists that all five specimens belong to the same species. (a) Examine the data. Make a scatterplot with femur length as the explanatory variable. Use your calculator to obtain the correlation r and the equation of the least-squares regression line. Do you think the femur length will allow good prediction of humerus length? (b) Explain in words what the slope β of the true regression line says about Archaeopteryx. What is the estimate of β from the data? What is your estimate of the intercept α of the true regression line? β represents how much we can expect the humerus length to increase when femur length increases by 1 cm, b (the estimate of β ) is 1.1969, and the estimate of α is a = 3.660. (c) Calculate the residuals for the five data points. Check that their sum is 0 (up to roundoff error.) Use the residuals to estimate the standard deviation σ in the regression model. You have now estimated all three parameters in the model. The residuals are 0.8226, 0.3668, 3.0425, 0.9420, and 0.9110; the sum is 0.0001 (but carrying a different number of digits might change this). Squaring and summing the residuals gives 11.79, so that 11.79/ 3 1.982. s = = The correlation is r = 0.994, and linear regression gives ˆ 3.66 0 1.1969 yx = - + The scatterplot below shows a strong, positive, linear relationship, which is confirmed by r .
3 14.2 BACKPACKS Body weights and backpack weights were collected for eight students. Weight (lbs): Backpack weight (lbs): 120 26 187 30 109 26 103 24 131 29 165 35 158 31 116 28 These data were entered into a statistics package and least-squares regression of backpack weight on body weight was requested. Here are the results: Predictor Constant BodyWT Coef 16.265 0.09080 Stdev 3.937 0.02831 t-ratio 4.13 3.21 P 0.006 0.018 s = 2.270 R-sq = 63.2% R-sq(adj) = 57.0% (a) What is the equation of the least-squares line? (Hint: Look for the column “Coef.” What is the intercept? What is the slope? backpack weight = 16.265 + 0.0908(body weight). The intercept is 16.265 and the slope is 0.0908 (b) The model for regression inference has three parameters, which we call α , β , and σ . Can you determine the estimates for α and β from the computer output? What are they? The estimate for α is the intercept of the least-squares line, that is, 16.265. The estimate for β is the slope of the least-squares line, that is, 0.0908.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.

### Page1 / 13

CH14 exercises solutions - X X X X X X X X X X X X X X X X...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online