If other factors are held constant, if the Pearson correlation between X and Y is r = 0.50, then the regression equation will produce more accurate predictions than would be obtained  if r = 0.70. True or false?

Q: True or false? If the statement is false, use one or two sentences to justify your answer.

A: The negative correlation indicates that the relationship between x and y is inverse in nature and…

Q: For a certain data set the regression equation is ý-29-5x. The correlation coefficient between y and…

A: Coefficient of correlation

Q: When the correlation coefficient, r, is close to one: a. There is no relationship between the two…

A: We know that,  The linear correlation (r) between X and Y two variables, the correlation values lies…

Q: 14. Consider the following regression equation: Y = 30 - 9X. If SSE = 600 and SS Total = 1,200, then…

A: The square of correlation coefficient is computed by r2=1-SSESST, where SSE is the error sum of…

Q: which of the following regressions represents the strongest negative linear relationship between x…

A: The correlation coefficient r is used to measure the linear relationship between two variables X and…

Q: A value of r close to 0 indicates that the regression equation is either useless or ______ for…

A: As the correlation value closer to 0, the coefficient of determination (R-square) will be decreased.…

Q: The Life Insurance Company is attempting to model the weight, Y (in pounds), of a random sample of…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose that you perform a hypothesis test for the slope of the population regression line with the…

A: It is given that the null hypothesis is rejected.

Q: If the correlation of the X's is equal to 1 or -1, then the regression cannot process. Why?

A: Correlation of X's means that the independent variables (IVs) are dependent on each other and this…

Q: if the total sum of squares of y is 32, the sum of squares of the regression line with respect to…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: Even if the error terms in the regression equation, H1,H_2,....,µ_n, are not normally distributed,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A sample of n = 15 pairs of X and Y scores produces a Pearson correlation of r = 0.45, SSY = 90. a)…

A:

Q: The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30…

A:

Q: Why is the null hypothesis for regression usually B 0?

A: The null hypothesis for regression usually β=0

Q: If we collect monthly sales over two years for N=100 stores, we should not apply a simple linear…

A: If we collect monthly sales over two years for N=100 stores, we should not apply a simple linear…

Q: If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot…

A: From the provided information, The hypotheses can be constructed as: H0: ρ = 0 (There is no…

Q: If the error term in a linear regression model is normally distributed, then the distribution of the…

A:

Q: If there is a positive correlation between X and Y then in the regression equation, Y = bX + a,…

A: Solution-: If there is a positive correlation between x and Y then in the regression equation,…

Q: If all actual values of the dependent variable lie on the estimated regression line, then the…

A: From the given information, All the actual values of dependent variable are lie on the straight…

Q: State True or False A linear regression with a[ostive correlation will have a slope that is greater…

A: Given : Statement : A linear regression with positive correlation will have a slope that is greater…

Q: What factors cause the standard error of the regression model to be smaller? Discuss at least 2

A: The factors which cause the standard error of the regression model to be smaller are discussed…

Q: The Linear regression is used to predict Y from X in a certain population. In this population, SSY…

A:

Q: I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive…

A: Given: The linear regression model, y=b0+b1x1+b2x2+e

Q: If the correlation coefficient is a positive value, then the slope of the regression line... O a.…

A: The correlation coefficient represents the direction and strength of the relationship between x and…

Q: A certain Instructor believes that the grades of students is related to the number of progress…

A:

Q: f there is a positive correlation between X and Y, then the regression equation Y = bX + a will have…

A: Correlation: Correlation analysis is used to measure the strength of the association between…

Q: Suppose two variables are under study are temperature in degrees Fahrenheit (y) and temperature in…

A: The given regression line is y=95x+32. The correlation coefficient is the ratio of the covariance…

Q: Suppose that you are modelling cooling costs (y) as a function of the daily high temperature (x) for…

A: Correlation is the measure of the strength of association between two variables. The value of…

Q: Given the equation of a regression line is y= -1.5x-1.8, what is the best predicted value for y…

A:

Q: Given the equation of a regression line is  y  = -5.5x - 9.4, what is the best predicted value for y…

A: Given,   The equation of a regression line is,

Q: As the value of correlation coefficient increases from 0 to 1, or decreases from 0 to -1, how do the…

A: It is known that the value of the correlation coefficient lies between -1 and 1. The value 1…

Q: If other factors are held constant and the Pearson correlation value between X and Y is r = 0.80,…

A: Correlation coefficient quantifies the strength and direction of relationship between variable. The…

Q: sion model are totally unrelated, _______. the coefficient of determination would be 0 the MSE…

A: Correlation is defined as the linear relationship between the two variables. The range of the…

Q: If a correlation is r= 0.00, then SP = 0 and the regression equation is O Ý =X +0 O Ý =X + X O Ý =0…

A: Given: correlation is r = 0.00, then SP = 0

Q: If the Pearson correlation between X and Y is negative, then the regression equation will have a…

A: Conditions based on sign with respect to the correlation coefficient and slope:   As the…

Q: What can you say about SSE, SSR, and the utility of the regression equation for making predictions…

A:

Q: A value of r close to _____ indicates that the regression equation is extremely useful for making…

A: Correlation: Correlation a measure which indicates the “go-togetherness” of two data sets. It can be…

Q: The correlation between first year college GPA and high school GPA is 0.683. If a simple linear…

A: Given information: The correlation between first year college GPA and high school GPA is 0.683. If a…

Q: Where we observe multicollinearity in a multiple regression analysis, two of our independent…

A:

Q: Suppose that a regression relationship is given by the following:Y = β0 + β1X1 + β2X2 + εIf the…

A: Given: Y = β0 + β1X1 + β2X2 + ε (a) In simple regression Y on X1 the intercept term will the…

Q: Show that arithmetic mean of regression coefficients is greater than the correlation coefficient.

A: Regression coefficients :  Let X and Y be two variables, then we can get two regression equations;…

Q: How to know if obtaining a regression equation for the data appear reasonable?

A: Linear regression: It is a method for predicting the value of a dependent variable Y , based on the…

Q: It is known that the linear regression equation: y= -2.88+1.77x, with a coefficient of determination…

A:

Q: f the Pearson correlation between X and Y is r = .50, then the regression equation predicts 25% of…

A: Obtain the value of the coefficient of determination.   The value of the coefficient of…

Q: Which of the following statements is true with respect to a simple linear regression model?  The…

A: We need to identify correct statements using concept of Simple linear regression

Q: Suppose that you perform a hypothesis test for the slope of the population regression line with the…

A: For the slope of the population regression equation, β1, hypotheses are stated as given below: Null…

Q: A fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y =…

A: Given,regression model is y^=10+2x if x=0 and the corresponding observed value of y=9

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.