1 of 3 Instructor: Erdil INDE6609 – Homework 5 Spring 2015 DESCRIPTIVE & INFERENTIAL STATISTICS HOMEWORK 5 Homework 5 for INDE6609 is designed to improve your understanding of regression analysis and analysis of single factor with three or more levels. The assignments problem is intended to help you learn to perform and interpret analysis of variance to test differences among means of several groups and to develop simple linear regression models; to assess model adequacy with residual plots; to use multiple comparison procedures to identify specific differences between means; and to make decisions using statistical analysis. Submission Guidelines: • Please specify clearly any assumptions that you make. • Provide manual or Minitab solutions to the problems. • Justify your explanations or recommended actions by using the output of visual data displays or numerical summaries. • Provide your solutions in one document prepared in word processor software. (Hard-written assignments will not be accepted) • Submit a copy of your assignment on Blackboard by the assignment due date. Five Questions (all questions equal weight): Q1.Establishing the properties of materials is an important problem in identifying a suitable for biodegradable materials in the fast-food packaging industry. Consider the following data on product density (g/cm3 ) and thermal conductivity K-factor (W/mK). Perform the following: a) Write the estimated regression line b) Compute the residuals c) Compute SSE and estimate the variance d) Find the standard error of the slope and intercept coefficients e) Compute and comment on the R2 value. f) Compute and comment on the significance of the intercept and slope coefficients at α = 0.05 g) Construct the ANOVA table and test for the significance of regression using the p-value. h) Construct 95% CIs on the intercept and slope. i) Perform model adequacy checks. Do you believe the model provides an adequate fit? Thermal Conductivity y Product Density x 0.0480 0.1750 0.0525 0.2200 0.0540 0.2250 0.0535 0.2260 0.0670 0.2500 0.0610 0.2765 2 of 3 Instructor: Erdil INDE6609 – Homework 5 Spring 2015 Q2. Consider the data given in Q1, and the simple linear regression found. a) Find the mean thermal conductivity given that the product density is 0.2350. b) Compute a 95% CI on this mean response c) Compute a 95% on a future observation when the product density is equal to 0.2350 d) What do you notice about the relative size of these two intervals? Which is wider and why? Q3. The following data (20 data points) represents the result of a study investigating relationship between noise exposure and hypertension. y 1 0 1 2 5 1 4 6 2 3 x 60 63 65 70 70 70 80 90 80 80 y 5 4 6 8 4 5 7 9 7 6 x 85 89 90 90 90 90 94 100 100 100 a) Draw a scatter diagram of y (blood pressure rise in millimeters of mercury) versus x (sound pressure level in decibels). Does a simple linear regression model seem reasonable in this situation? b) Fit the simple linear regression model using least squares method. Find an estimate of σ2 . c) Find the predicted mean rise in blood pressure level associated with a sound pressure level of 85 decibels. Q4. Use the following partially complete Minitab output to answer the following questions. a) Find all of the missing values. b) Find the estimate of σ2 . c) Construct a 95% confidence interval on β1. Use this CI to test for significance of regression. Predictor Coef SE Coef T P Constant 0.6649 0.1594 4.17 0.001 X 0.83075 0.08552 ? ? S=? R-Sq = 88.7% R-Sq = 87.8% Analysis of Variance Source DF SS MS F P Regression 1 3.6631 3.6631 ? ? Residual Error 12 0.4658 ? Total 13 ? 3 of 3 Instructor: Erdil INDE6609 – Homework 5 Spring 2015 Q5. The tensile strength of a synthetic fiber is of interest to the manufacturer. It is suspected that strength is related to the percentage of cotton in the fiber. Five levels of cotton percentage are used, and five replicates are run in random order, resulting in the data that follow. Does cotton percentage affect breaking strength? Draw comparative box plots and perform an analysis of variance. Use a P-value approach. Observations Cotton Percentage 1 2 3 4 5 15 7 7 15 11 9 20 12 17 12 18 18 25 14 18 18 19 19 30 19 25 22 19 23 35 7 10 11 15 11