Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity (i.e. high correlation amongindependent variables) with variablesyx1x2x3x4x5O x1 and yO x2 and x5O x1 and x5O x3 and x5Oy and x4y10.954168-0.11828-0.120030.925901-0.18105x11-0.00383-0.084990.118169-0.07371x21-0.14523-0.148760.995886x310.050042-0.14151x41-0.16934x51

Answered: Image /qna-images/answer/0e710ce8-8ac9-4656-ab67-c546a0e12204.jpg

Answered: Inspection of the following table of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Simple linear regression results: Dependent Variable: Heart. DiseaseIndependent Variable: BikingHeart. Disease = 18.115809 - 0.20845321 BikingSample size: 68R (correlation coefficient) = -0.94616452R-sq = 0.8952273Estimate of error standard deviation: 1.5273175 Correlation between Biking and Heart. Disease is: -0.94616452. Correlation between Smoking and Heart. Disease is: 0.32421. 1) State r 2 (i.e., the coefficient of determination) for “Biking” and “Heart.Disease” and explain what this value means in context of the data set.
True/false (please explain). Suppose that a regression of Y on X₁ is unbiased, and the true slope coefficient is 2. Another variable X2 is correlated with Y, but it is uncorrelated with X₁. In expectation, the default t-statistic on B₁ will be larger in the multivariate regression that includes X₂ than in the bivariate regression that omits X₂.
2. A study is conducted in patients with HIV. The primary outcome is CD4 cell count which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to use of supplements(coded as l ves, 0-no) and to duration of HIV, in years(ie., the number of years between the diagnosis of HIV and the study date). For the analysis, Y-CD4 count. Y 501.41 12.67 Supplements - 30.23 Duration of HIV A. What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years? B. What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment? C. What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years
uppose IQ scores were obtained from randomly selected couplescouples. For 2020 such pairs of people, the linear correlation coefficient is 0.8900.890 and the equation of the regression line is ModifyingAbove y with caret equals negative 0.74 plus 1.02 xy=−0.74+1.02x, where x represents the IQ score of the husbandhusband. Also, the 2020 x values have a mean of 101.17101.17 and the 2020 y values have a mean of 102.7102.7. What is the best predicted IQ of the wifewife, given that the husbandhusband has an IQ of 9999? Use a significance level of 0.05. The best predicted IQ of the wifewife is nothing. (Round to two decimal places as needed.
If Linear correlation coefficient r = 0.794556 Coefficient of determination = 0.631319 Equation of regression line is y = 16.5523 + %3D 0.725938x then both variables are moving in the same direction. A True В False
Data on 11 randomly selected athletes was obtained concerning their cardiovascular fitness (measured by time to exhaustion running on a treadmill) and performance in a 20-km ski race. Both variables were measured in minutes and a regression analysis was performed. Ski 88 2.5 . Treadmill Coefficients Estimate Std. Error 0.41 (Intercept) Treadmill 1.11 88 -2.5 Is there sufficient evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance? (a). The test statistic is (b). The p-value is (use four decimal places) (use four decimal places) (c). At the 2% significance level, we Select an answer the null hypothesis and conclude that there is Select an answer evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance.
Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(
A researcher developed a regression model to predict the tear rating of a bag of coffee based on the plate gap in bag-sealing equipment. Data were collected on 28 bags in which the plate gap was varied. An analysis of variance from the regression showed that b, = 0.7909 and Sp. = 0.2294. a. At the 0.05 level of significance, is there evidence of a linear relationship between the plate gap of the bag-sealing machine and the tear rating of a bag of coffee? b. Construct a 95% confidence interval estimate of the population slope, B1. .....
From the article “Association of cognitive functioning with retinal nerve fiber layer thickness” by van Koolwijk et al., in Investigative Ophthalmology & Visual Science, October 2009, Vol. 50, No. 10, below is table 2 showing the results of fitting several multiple linear regression models for different response variables. Write down the fitted model corresponding to the last row of the table. You can leave the intercept as hatB0. Interpret the coefficient values corresponding to the RNFL Thickness and Male variables.
A researcher is interested in examining the relationship between spousal abuse and child abuse. Specifically, they are interested in determining whether there is a predictive relationship between spousal abuse and child abuse in 5 county social services offices. Calculate the linear regression line for the following data. Note you have already calculated the first step to this analysis (Pearson's Correlation)
7.Why is the strength of the correlation between Y and X important in regression analysis?
Police sometimes use footprint evidence to estimate the height of a suspect. Data was collected from 36 randomly selected men in Nebraska in 2001. The regression model assumptions have been checked, and they are all satisfied. We want to test if there is a positive linear association between shoe print size and average height. The p-value of the appropriate test was found to be 0.0006. (a) Give your brief conclusion. Note that no significance level is provided. (b) Give your conclusion in the context of the problem. (This question will be marked manually by your instructor).

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