Question

Which of the following statements concerning the linear correlation coefficient are true? I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies between -1 and 1. IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. A) II and III B) I and II C) I and IV D) III and IV Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.523, n = 25 A) Critical values: r = plusminus 0.396, significant linear correlation B) Critical values: r = plusminus 0.487, no significant linear correlation C) Critical values: r = plusminus 0.396, no significant linear correlation D) Critical values: r = plusminus 0.487, significant linear correlation Write the word or phrase that best completes each statement or answers the question. Construct a scatterplot for the given data. Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

Answer 1

Answer:

1) A) II and III

2) A) Critical values: r = plusminus 0.396, significant linear correlation

3) Yi= 0.41 + 0.37Xi

Step-by-step explanation:

Hello!

The objective of the linear correlation analysis is to test if there is an association between two study variables (X₁ and X₂).

Pearson's Coefficient of correlation

For Variables with a bivariate normal distribution (X₁, X₂)~N₂(μ₁; μ₂; σ₁²; σ₂²; ρ)

To do so, the study parameter is the population coefficient of correlation (ρ) - Rho- (If you were to make a graphic of the correlation line, Rho represents the slope)

Sample coefficient of correlation: r

It takes values between -1 and 1

This coefficient gives an idea of ​​the degree of correlation between the variables.

If ρ = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is cero

If ρ < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If ρ > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)

The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables. For example, if you were to have two coefficients r₁= -0.24 and r₂= 0.67 then the absolute values are Ir₁I= 0.24 and Ir₂I= 0.67 you can see that the coefficient of the second sample is bigger than the first sample, that means that there is a stronger correlation in the second sample than the first one.

The non-parametric coefficient of correlation has the same characteristics.

1) Statements:

I: If the linear correlation coefficient for the two variables is zero, then there is no relationship between the variables. FALSE, when r=0 then there is no linear association between the two variables, this doesn't mean that there isn't any other type of association between them.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. TRUE

The regression and correlation analyses are closely linked because for a regression equation to be reasonable, the sample points must be linked to the equation and the correlation coefficient between both variables must be large when the degree of association is high and small when The degree of association is low in addition to being independent of the units.

The regression analysis tests whether or not there is an association between both variables and the correlation analysis indicates the degree of that association.

If the slope of the regression is negative, then the correlation coefficient is negative.

III: The value of the linear correlation coefficient always lies between -1 and 1. TRUE, it is one of the characteristics of the correlation coefficient.

0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. FALSE, to check wich correlation coefficient shows a stronger correlation look at their absolute values, the one that is closer to 1 is the stronger, Ir₁I= 0.62 < Ir₂I= 0.82

Correct answer:

A) II and III

2) Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.523, n = 25

For this, you have to use a Table of cumulative probabilities for the linear correlation coefficient. (I've used Pearson)

For a two-tailed test (H₀: ρ=0)

$r_{n-2; \alpha/2}= r_{23; 0.025}=$ ± 0.396

Against r = 0.523, the decision is to reject the null hypothesis. There is a linear correlation between the two study variables.

Correct answer:

A) Critical values: r = plus-minus 0.396, significant linear correlation

3) Construct a scatterplot for the given data. Check 1st attachment for Data and Scatterplot.

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

Equation of regression:

Yi= a + bXi

a= $(\frac{sum Yi}{n})$+b$(\frac{sum Xi}{n})$

b= $\frac{sum XiYi*\frac{(sum Xi)(sum Yi)}{n} }{/(sumXi^2)-\frac{(sumXi)^2}{n} }$

Using the given Data:

∑Xi= -11

∑Xi²= 201

∑Yi= 0

∑Yi²= 176

Mean X= -1.10

Mean Y= 0

a= 0.41

b= 0.37

Yi= 0.41 + 0.37Xi

4) Managers rate empoyees acording to job performance and attitude. The results fro several randomly selected empoyees are given below.

Performance: 59; 63; 65; 69; 58; 77; 76; 69; 70; 64

Attitude: 72; 67; 78; 82; 73; 87; 92; 83; 87; 78

No question found?

I hope it helps!