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- For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.arrow_forwardConsider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.arrow_forwardWhich of the scatter diagrams below suggests a strong positive linear relationship between the x and y variables?arrow_forward
- A researcher interested in the correlation between family size X annual income Y and parental education level Z produces the following correlation matrix x. y. z x +1.00. +0.32. +0.56 y. +0.32. +1.00. +0.88 z. +0.56. +0.88. +1.00 What is the correlation between annual income and parental education level?arrow_forwardSuppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation coefficient of 0.454012. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1503.578103 Sx = 107.836402 y freshman year GPA y = 3.299812 Sy = 0.517403 r = 0.454012 Determine the slope, b, of the least squares regression line for this data. Give your answer precise to four decimal places. Avoid rounding until the last step. b %Darrow_forward2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.arrow_forward
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- Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation coefficient of 0.503202. Additional sample statistics are summarized in the table below. Variable Variabledescription Samplemean Sample standarddeviation ?x high school SAT score ?⎯⎯⎯=x¯= 1501.717708 ??=104.141305sx=104.141305 ?y freshman year GPA ?⎯⎯⎯=3.300318y¯=3.300318 ??=0.451901sy=0.451901 ?slope=0.503202=0.002184r=0.503202slope=0.002184 Determine the ?y‑intercept, ?a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places.arrow_forwardConsider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i 1,..., n.arrow_forwardLet X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,