4. Let X1, X2, X3, X4 denote the variables bill length, bill depth, flipper length and body mass,respectively. Suppose that we introduce two new variables: Y1 = 3X1 + 2X2 and Y2 = X2 + X3 + X4.Let Y be the dataset recording variables Y1 and Y2 of the same individuals as in X. Find the meanvector and covariance matrix of Y.

x1 x2 x3 x4 bill_length_mm bill_depth_mm flipper_length_mm body_mass_g y1 y2 3x1+2x2…

Answered: 4. Let X1, X2, X3, X4 denote the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y) 6.22 −0.08 8.01 0.25 8.67 −0.14 10.61 0.00 12.5 0.08 11.94 0.03 12.55 −0.07 17.93 0.29 18.34 0.23…
A computer while calculating the correlation coefficient between the variables X and Y obtained the following results: N= 30, ΣΧ-120, ΣΧ600, ΣΥ-90, ΣΥ250, ΣΧΥ-356. It was, however later discovered at the time of checking that it had copied down two pairs of observations: X Y wrongly as while the correct values are X Y 8 10 8 12 10 8 12 7. Find the correct value of correlation coefficient between X and Y.
A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. How would the value of the correlation coefficient, r, change if sodium was plotted on the x-axis and calories plotted on the y-axis? The value of r would increase. The value of r would not change. The value of r would change to –0.83. The value of r could increase or decrease, depending of the strength of the new relationship.
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 0.481202. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1495.716802 Sx = 109.915203 y freshman year GPA y = 3.260911 Sy 0.492802 r = 0.481202 slope = 0.002157 Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places. a =
Which scatterplot shows a nonlinear association?
1 Professor Yema conducted a research to determine factors that influence environmental attitude. Table 1 below is a matrix of Pearson’s r correlation coefficients for the following variables used in the study: Environmental attitude (En), level of education (Le), and income (In). Table 1: Factors that influence environmental attitude ____________________________________________________________________ Variable En Le In ____________________________________________________________________ Environmental attitude (En) 1.0 Level of education (Le) 0.6** 1.0 Income (In) –0.3* 0.9*** 1.0 ____________________________________________________________________ ***Correlation is…
An "extraneous variable" is not a problem unless it with the independent variable O is identical systematically co-varies is not correlated Wait! An "extraneous variable" is by definition never a problem, that's what "extraneous" means.
Which of the following scatter plots that true linear association?
A correlation coefficient might not have an appropriate relationship between two variables. This can happen between two variables when A. it is highly scattered B. is nonlinear is some way C. has a directionality problem

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