18 A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a cross section of the brain) and IQ (4 performance scales of the Wechsler IQ test)for college students. The data comprise of the variables, Performance IQ scores (IQ) and Brain Size (Size) and were analyzed in a linear regression model.Use the StatCrunch output to answer the following question.Simple linear regression results:Dependent Variable: IQIndependent Variable: SizeIQ-1.743757 +0.0001202538 SizeSample size: 40R (correlation coefficient) - 0.38681732R-sq-0.14962764Estimate of error standard deviation: 20.992707Which of the following best describes the data?There is a moderate linear association in the negative direction.There is a moderate linear association in the positive direction.There is a strong linear association in the negative direction.There is a strong linear association in the positive direction.

We know The value of correlation coefficient decide (association and direction) for correlation.…

Answered: A study examined brain size (measured…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 2ECP

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The monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…
A mail-order business selling personal computer supplies, software and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect the warehouse distribution costs. Data collected over 24 random months contain the warehouse’s distribution cost (in thousands of Rands), the sales (in thousands of Rands) and the number of orders received. A multiple linear regression model was fitted to the data by using Stat1.2. Use the output to answer the questions that follow by typing only the letter of the correct option in the answer boxes. Variablesy: Warehouse Distribution Costx1: Salesx2: Number of Orders Model Fitting StatisticsR2 = 0.8504Adj R2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates…
Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below. Say how you know from the output that there actually is a significant linear relationship between a male customer’s age at death and his father’s age at death. State the value of the coefficient of Father’s Age (Death) and interpret this value in the context of the problem at hand.State the value of the coefficient of determination in the model and interpret this value in the context of the situation.
Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below Examine both the scatterplot and the correlation matrix provided above. Comment on the apparent relationship between the customer’s age at death and their father’s age at death in the plot. Explain how the information in the correlation matrix supports your conclusion
A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain. MPG HORSEPOWER WEIGHT 44 67 1,844 44 50 1,998 40 62 1,752 37 69 1,980 37 66 1,797 34 63 2,199 35 90 2,404 32 99 2,611 30 63 3,236 28 91 2,606 26 94 2,580 26 88 2,507 25 124 2,922 22 97 2,434 20 114 3,248 21 102 2,812 18 114 3,382 18 142 3,197 16 153 4,380 16 139 4,036
A statistics consulting center at a major university analyzed data on normal woodchucks for the university's veterinary school. The variables of interest were body weight in grams and heart weight in grams. It was desired to develop a linear regression equation in order to determine if there is a significant linear relationship between heart weight and total body weight. Use this information to answer the questions. Determine the test statistic. Body Weight Heart Weight4050 11.12435 10.13135 15.85740 10.92555 10.73665 11.42035 13.44260 13.92990 11.54935 15.83690 10.12880 12.82760 10.62160 15.42360 14.82040 13.62055 12.92650 15.62665 13.8
Develop an estimated multiple linear regression model that could be used to predict the alumni giving rate using the graduation, % of Classes Under 20 (LT20), and Student/Faculty Ratio (SFR) as independent variables. Discuss your findings. School SFR LT20 GT50 GRAD FRR GIVE Arizona State 24 42% 16% 59% 81% 8% Arkansas State—Jonesboro 19 49% 4% 37% 69% 11% Auburn 18 24% 17% 66% 87% 31% Air Force 8 74% 0.10% 81% 88% 11% Military Academy 8 95% 0% 86% 92% 28% Akron 20 39% 6% 35% 69% 15% Arizona 20 35% 17% 60% 79% 5% Arkansas 18 28% 18% 58% 83% 23% Ball State 18 34% 12% 57% 78% 11% Baylor 14 49% 9% 71% 85% 14% Boise State 21 33% 11% 27% 67% 8% Boston College 14 47% 6% 91% 96% 27% Bowling Green State 19 33% 7% 61% 75% 8% BYU 21 46% 12% 78% 84% 17% SUNY 16 36% 21% 67% 88% 9% Alabama 19 46% 16% 67% 85% 34% Central Michigan 22 32% 11% 54% 78% 8% Clemson 16 51% 13% 76% 91% 28% Colorado State 18 34% 19% 64% 83% 7% Berkley 17 62% 15% 91% 97% 12%…
King & Scott, a research firm for the real estate industry, studied the relation between x=x= annual income (in thousands of dollars) and y=y= sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table. Annual Income House Price 72 188 48 91.6 73 182.2 97 155.5 97 238.8 94 203.4 67 160.1 85 212 64 169 Conduct a linear regression. Use the results to answer the following questions. a. What is the value of the correlation coefficient (round to 3 decimal places)? What does the value tell you about the linear relationship between the annual income and the price of house purchased? Correlation coefficient: This indicates: very weak positive linear correlation fairly strong negative linear correlation perfect positive linear correlation very weak negative linear correlation perfect negative linear correlation no linear…
When a regression coefficient in a multiple linear regression model is zero, the slope of the corresponding independent variable is zero. True False
A researcher was investigating variables that might be associated with the academic performance of high school students. The data included the average Math SAS score of all high school seniors in the city that took the exam (labeled as the variable SAT-M), the average number of dollars per pupil spent on education by the city (labeled as the variable $Per Pupil), and the percentage of high school seniors in the city that took the exam (labeled as the variable %Taking). The researcher ran the following multiple linear regression model as SAT-M=Beta0 + Beta1($Per Pupil) + Beta2(%Taking). This model was fit to the data using the method of least-squares, results shown inside of table within photo. If we want to test using ANOVA F-test with hypotheses Ho: Beta1=Beta2=0 versus H1: at least one of the Beta is not 0, what would the value of our F-statistic mean?
If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?
The Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?

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