Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: x = Temperature (°C) 1100 1200 1300 1100 1500 1200 1300 30.8 19.2 6 13.5 11.4 7.7 3.6 y = Porosity (%) (a) Fit the simple linear regression model using the method of least squares. Find the least squares estimates of the intercept and slope in the simple linear regression model. Find an estimate of o². Bo= (Round your answer to 3 decimal places.) B₁ = (Round your answer to 5 decimal places.) (Round your answer to 2 decimal places.) i (b) Estimate the mean porosity for a temperature of 1409 °C. ŷ = i (Round your answer to 2 decimal places.)

Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: x = Temperature (°C) 1100 1200 1300 1100 1500 1200 1300 30.8 19.2 6 13.5 11.4 7.7 3.6 y = Porosity (%) (a) Fit the simple linear regression model using the method of least squares. Find the least squares estimates of the intercept and slope in the simple linear regression model. Find an estimate of o². Bo= (Round your answer to 3 decimal places.) B₁ = (Round your answer to 5 decimal places.) (Round your answer to 2 decimal places.) i (b) Estimate the mean porosity for a temperature of 1409 °C. ŷ = i (Round your answer to 2 decimal places.)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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Consider the multiple regression model to investigate the relationship between the number of fishes (Y) per section of the stream and the following independent variables: dissolved oxygen (3 < oxy < 10, in mg/liter), maximum depth (1 < maxdepth < 8, in feet), and water temperature (5< temp < 20, in °C). The location of the stream was also considered (lowland and upland). Y-hat = 23.09 + 0.199*oxy + 0.3361*maxdepth +8.6730*temp + 3.8290* lowland. Which of the following is(are) TRUE about the estimated regression coefficient for location of the stream? 1. The location of the stream is a categorical variable, so it is represented by a dummy variable with upland stream as the reference variable. II. Holding other factors constant, the number of fishes in lowland is 3.8290 higher than upland streams. O A. I only O B. II only O C. Both I and II O D. Neither I nor II
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The scatter plot below shows the average cost of a designer jacket in a sample of years between 2000 and 2015. The least squares regression line modeling this data is given by yˆ=−4815+3.765x. A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price ($) from 2660 to 2780 in increments of 20. The following points are plotted: (2003, 2736); (2004, 2715); (2007, 2675); (2009, 2719); (2013, 270). All coordinates are approximate. Interpret the slope of the least squares regression line. Select the correct answer below: 1.The average cost of a designer jacket decreased by $3.765 each year between 2000 and 2015. 2.The average cost of a designer jacket increased by $3.765 each year between 2000 and 2015. 3.The average cost of a designer jacket decreased by $4815 each year between 2000 and 2015. 4. The average cost of a designer jacket increased by $4815 each year between 2000 and…
4
The data in the accompanying table include the appraised value, land area of the property in acres, and age, in years, for a small sample of 30 single-family homes in a small city. Perform a multiple regression analysis to predict appraised value based on land area of the property X1 and age, in years, X2 and determine the VIF for each independent variable in the model. Is there reason to suspect the existence of collinearity? Determine the VIF for each independent variable in the model.
Miniature horses are a special breed of very very small horse. A minuature horse breeder is interested in the relationship between the size (height) of a miniature horse (x, in mm) and the price it sells for (y, in $). She decides to fit the simple linear regression model: E(y) = β0 + β1x A regression analysis using the heights and sale prices of 60 miniature horses gave the following results: Estimated slope coefficient (estimate for β1) = -7.0Standard error for the slope coefficient = 4.0Test statistic for the slope coefficient t = 1.750, to 3 decimal places, n-2 = 58 dfP-value for the slope coefficient = 0.08541 (to 5 decimal places). Is there significant evidence, at (alpha) α = 0.05, of a linear relationship between the size (height) of a miniature horse (x, in mm) and the price it sells for (y, in $). ? What is your conclusion? a. yes b. no