Suppose that a scientist takes experimental data on the radius of a propellant grain Y as a function of powder temperature x₁, extrusion rate X2, and die temperature x3. The accompanying data set is available below. Complete parts (a) and (b) below. Click here to view the coded data. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) A case can be made for eliminating x₁, powder temperature, from the model since the P-value based on the F-test is 0.3488 while P-values for X₂ and x3 are near zero. Reduce the model by eliminating x₁, thereby producing a full and a restricted (or reduced) model, and compare them on the basis of R2 adj The full model is y = 127.50 + (1.25)x₁+ (18.25¹) x₂ + (26.25") (Round to two decimal places as needed.) The restricted model is y = 127.50 +(18.25) x₂ + (26.25) X3. (Round to two decimal places as needed.) X3. For the full model, R² = 0.991, for the restricted model, R² = 0.990, so there appears to be adj adj model. a small advantage when using the full (Round to three decimal places as needed.) (b) Compare the full and restricted models using the width of the 95% prediction intervals on a new observation. The better of the two models would be that with the tightened prediction intervals. Use the average of the width of the prediction intervals. For the full model, the average width is 22.68. For the restricted model, the average width is 20.35¹. So, the model without x, appears to be the better model. (Round to two decimal places as needed.)

The accompanying data represent the total compensation for 12 randomly selected chief executive officers (CEOS) and the company's stock performance. Use the data to complete parts (a) through (d). E Click the icon to view the data table. (a) Treating compensation as the explanatory variable, x, use technology to determine the estimates of Bo and B,- The estimate of B, is (Round to three decimal places as needed.) Data Table of Compensation and Stock Performante Compensation Company (millions of dollars) Return (%) O Stock A 14.71 75.73 В 4.02 64.29 C 6.55 141.81 D 1.32 30.73 1.73 10.75 2.43 29.05 12.26 0.56 7.07 66.32 9.51 56.31 J 3.83 58.48 K 21.29 21.52 6.63 31.85 Print Done

Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 400 392 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total R-Sq= 98.5% DF SE Coef 2.483 6.464 1 9 10 SS 7639.0 117.0 7756..0 T 129.64 24.24 P 0.000 0.000. R-Sq (adj) 98.3% MS 7639.0 13.0 F 587.81 (a) Does the simple linear regression model appear to be appropriate?…

No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on x = frying time (sec) and y = moisture content (%) appeared in an article. x 5 10 15 20 25 30 45 60 y 16.4 9.7 8.1 4.2 3.3 2.8 2.0 1.2 (a) Construct a scatter plot of y versus x. y 15 10- 5 y 15 O 10 10 20 30 40 50 5 10 20 10 NE X 50 60 30 60 40 X 15 y 10 O 5 O y 15 10 20 30 40 50 60 10 20 30 Comment. The plot has a curved pattern. A linear model would not be appropriate. O The plot has a curved pattern. A linear model would be appropriate. O The plot does not have a curved pattern. A linear model would be appropriate. O The plot does not have a curved pattern. A linear model would not be appropriate. 40 50 60 X X

Q1: The data points below are related to a chemi-thermo-mechanical pulp from mixed density hardwoods. They relate Y (specific surface area of the fibres in cm/g) to the % NaOH (sodium hydroxide) used as a pretreatment chemical and the treatment time (min) for different batches of pulp. The variables are present at three different levels. In this case, it is preferred (for reasons that we will discuss later in the course) to code the levels as shown in the last two columns of the table below, designated by Xı and X2. Y SODIUM ΤΙME Xi X2 HYDROXIDE 5.95 3 30 -1 5.60 3 60 -1 5.44 3 90 -1 1 6.22 9. 30 -1 5.85 9 60 5.61 9. 90 1 8.36 15 30 1 -1 7.30 15 60 1 6.43 15 90 1 1 a. Using the variables Y, X1 and X2 (not actual time and sodium hydroxide! You will see why later!), fit the following multiple linear regression model to the data: (Model A) Y = (b0) + (b1) X1 + (b2) X2; subsequently, estimate the parameters and examine the residual plot (residuals vs Y hat). What does this residual plot…

pan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. An article reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). The following data was read from a graph in the article. x 125.8 98.1 201.4 147.3 145.9 124.7 112.2 120.2 161.2 178.9 159.5 145.8 75.1 151.5 144.2 125.0 198.8 133.9 y 77.9 76.8 81.5 79.8 78.2 78.3 77.5 77.0 80.1 80.2 79.9 79.0 76.9 78.2 79.5 78.1 81.5 71.0 (a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.)slope: intercept: (b) Does there appear to be a useful linear relationship? Carry out a test using the ANOVA approach and a significance level of 0.05. State the appropriate null and alternative hypotheses.…

Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".† x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total SE Coef 2.483 6.464 R-Sq = 98.5% DF 1 9 10 SS 7639.0 117.0 7756.0 T 129.64 24.24 0.000 0.000 R-Sq (adj) = 98.3% MS 7639.0 13.0 F P 587.81 (a) Does the simple linear regression model appear to be…

A process is monitored for defective items by taking a sample of 200 items each day and calculating the proportion that are defective. Let p; be the proportion of defective items in the ith sample. For the last 30 samples, the sum of the proportions is E P; = 1.64. Calculate the center line and the 30 upper and lower control limits for a p chart.

5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?

For a MR model with 4 predictors, we have: SSE 288 and SST = 957 What percentage of the variation in Y is accounted for by its assumed relationship with the predictors?