Concept explainers
Utilization of sucrose as a carbon source for the production of chemicals is uneconomical. Beet molasses is a readily available and low-priced substitute. The article “Optimization of the Production of b-Carotene from Molasses by Blakeslea Trispora” β. of Chem. Tech. and Biotech., 2002: 933–943) carried out a multiple
Obs | Linoleic | Kerosene | Antiox | Betacaro |
1 | 30.00 | 30.00 | 10.00 | 0.7000 |
2 | 30.00 | 30.00 | 10.00 | 0.6300 |
3 | 30.00 | 30.00 | 18.41 | 0.0130 |
4 | 40.00 | 40.00 | 5.00 | 0.0490 |
5 | 30.00 | 30.00 | 10.00 | 0.7000 |
6 | 13.18 | 30.00 | 10.00 | 0.1000 |
7 | 20.00 | 40.00 | 5.00 | 0.0400 |
8 | 20.00 | 40.00 | 15.00 | 0.0065 |
9 | 40.00 | 20.00 | 5.00 | 0.2020 |
10 | 30.00 | 30.00 | 10.00 | 0.6300 |
11 | 30.00 | 30.00 | 1.59 | 0.0400 |
12 | 40.00 | 20.00 | 15.00 | 0.1320 |
13 | 40.00 | 40.00 | 15.00 | 0.1500 |
14 | 30.00 | 30.00 | 10.00 | 0.7000 |
15 | 30.00 | 46.82 | 10.00 | 0.3460 |
16 | 30.00 | 30.00 | 10.00 | 0.6300 |
17 | 30.00 | 13.18 | 10.00 | 0.3970 |
18 | 20.00 | 20.00 | 5.00 | 0.2690 |
19 | 20.00 | 20.00 | 15.00 | 0.0054 |
20 | 46.82 | 30.00 | 10.00 | 0.0640 |
a. Fitting the complete second-order model in the three predictors resulted in R2 = .987 and adjusted R2 = .974, whereas fitting the first-order model gave R2 = .016. What would you conclude about the two models?
b. For x1 = x2 = 30, x3 = 10, a statistical software package reported that
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Chapter 13 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table: Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of Sigma2? What is the estimate of expected stem usage when the average temperature is 55 F? What change in mean stem usage is expected when the monthly average temperature changes by 1 F? Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. Test for significance of regression using α=0.01 (Use ANOVA). Calculate the r2 of the model. Find a 99% CI for B1 .arrow_forwardWhich of the following is(are) TRUE if the coefficient of determination between the response and the predictor variables is 0.81 based on a random sample of size n. O B. The Pearson's sample correlation coefficient is +0.9. O A. This means that 19% of the total variation in the response variable remains unexplained by the simple linear regression model that uses the given predictor variable. O Both A and B Neither A nor Barrow_forwardIn an attempt to develop a model of wine quality as judged by wine experts, data was collected from 50 red wine variants of a certain type of wine. A multiple linear regression model to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent) was developed, based on alcohol content (%), X1, and the amount of chlorides, X2. Perform a multiple regression analysis 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, with VIF1 and VIF2 being the VIF for X1 and X2, respectively.arrow_forward
- Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. t HRT Use Breast Cancer Incidence 46.30 40.60 39.50 36.60 30.00 103.30 105.00 100.00 93.80 83.50 (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ŷ = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer incidence (in cases per 100,000 women) would be…arrow_forwardThe following table gives the ages of female students in school and the corresponding Body Mass index (BMI) of 8 randomly selected students.(α=0.05) Age24223032211925 BMI27283029282726 Determine whether ages and BMI are significantly related.Determine the coefficient of linear determination and Intepret.Set up a linear regression equation to predict body mass index from age of students.Predict the body mass index of student who has the age of 26 years.arrow_forwardConsider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2arrow_forward
- The cotton aphid poses a threat to cotton crops in Iraq. The accompanying data on y = infestation rate (aphids/100 leaves) X1 = mean temperature (°C) x, = mean relative humidity appeared in the article “Estimation of the Economic Threshold of Infestation for Cotton Aphid" (Mesopotamia Journal of Agriculture [1982]: 71–75). Use the data to find the estimated regression equation and assess the utility of the multiple regression model y = a + Bjx1 + Bx2 + e y X1 X2 y X1 X2 61 21.0 57.0 77 24.8 48.0 87 28.3 41.5 93 26.0 56.0 98 27.5 58.0 100 27.1 31.0 104 26.8 36.5 118 29.0 41.0 102 28.3 40.0 74 34.0 25.0 63 30.5 34.0 43 28.3 13.0 27 30.8 37.0 19 31.0 19.0 14 33.6 20.0 23 31.8 17.0 30 31.3 21.0 25 33.5 18.5 67 33.0 24.5 40 34.5 16.0 34.3 6.0 21 34.3 26.0 18 33.0 21.0 23 26.5 26.0 42 32.0 28.0 56 27.3 24.5 60 27.8 39.0 59 25.8 29.0 82 25.0 41.0 89 18.5 53.5 77 26.0 51.0 102 19.0 48.0 108 18.0 70.0 97 16.3 79.5 Given: significance level = 0.05 Required: 1. Regression Equation 2. F and…arrow_forwardOne is interested in the ceteris paribus relationship between the dependent variable y, and the explanatory variable ₁1. For this, one collects data on two control variables Xi2 and Xiz and runs two LS regressions. Regression 1: yi = B₁x₁1 + Ui Regression 2: y = B₁xil+ B₂x₁2 + B3x13 + Ei Let ₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. a) Would you expect a difference between ₁ and ₁ when is highly correlated with 2 and 3 and the partial effects of xi2 and xi3 on yi are also high? b) Would you expect a difference between ₁ and 3₁ when ₁ has almost no correlation with and Xi3 but X2 and 3 are highly correlated? Xi2 c) Which of the two estimators is more efficient if x₁1 is highly correlated with 2 and 13, and Xiz have small partial effects on yi? but i2 d) Which of the two estimators is more efficient if x₁1 is almost uncorrelated with 2 and…arrow_forwardHormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. HRT Use Breast Cancer Incidence 46.30 103.30 40.60 105.00 39.50 100.00 36.60 93.80 30.00 83.50 n USE SALT (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ý = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer incidence (in cases per 100,000 women)…arrow_forward
- Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. HRT Use Breast Cancer Incidence 46.30 103.30 40.60 105.00 39.50 100.00 36.60 93.80 30.00 83.50 n USE SALT (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ý = 45.5727 + (1.3354 )x (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) 1.3354 cases per 100,000 women (c) What breast cancer incidence…arrow_forwardA baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown. Variable DF Estimate SE Intercept 1 16 2.073 Intentional Walks 1 0.50 0.037 R-sq=0.63R-sq=0.63 Let β1β1 represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A tt-test for a slope of a regression line was conducted for the following hypotheses. H0:β1=0Ha:β1≠0 below are the options provided thank youarrow_forward3. Wine Participant magazine has collected average price per bottle for the prestigious Chateau Le Thundebird bordeaux for different vintages (years). The data appears in the table below. year of bottling price a) draw the scatter diagram showing how wine price varies by vintage year b) use the most appropriate regression equation to determine the relationship between year of bottling (age) and price. c) what is the explanatory power (RSQ) of that equation d) determine the predicted price of a bottle of this wine for the 2017 vintage. 2009 36 2010 40 2011 51 2012 60 2013 68 2014 72 2015 70 2016 65 2018 51 2019 44 2020 39arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt