The lines of regression of a bivariate population are 8X – 10Y + 66 = 0 40X – 18Y = 214 The variance of X is 9. Find (i) The mean value of X and Y (ii) Correlation coefficient between X and Y (iii) Standard deviation of Y
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- Two lines of regression are given by 5x+7y-22=0 and 6x+2y-22=0. If the variance of y is 15, find the standard deviation of x.A sample of n = 25 pairs of scores (X and Y values) produces a correlation of r = –0.40. Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the α = 0.05 level of significance. Which proportion of the variance for the Y scores is predicted by the regression equation?If the Pearson correlation between X and Y is r = .50, then the regression equation predicts 25% of the variance in the Y scores. True or false? Why?
- The Linear regression is used to predict Y from X in a certain population. In this population, SSY is 50, the correlation between X and Y is .5, and N is 100. What will be the standard error of the estimate?After performing a statistical regression on a set of data the value of the correlation coefficient r was -0.2041. What does that imply about the data?If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that y and x are positively correlated.
- Can we proceed with regression if the correlation coefficient is zero? Why?If other factors are held constant and the Pearson correlation value between X and Y is r = 0.80, then the regression equation will tend to produce more accurate predictions than would be obtained if the Pearson correlation value was r = 0.60. True or FalseA set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.
- A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14. Find the standard error of estimate for the regression equation. What percentage of the variance in Y is accounted for by X?I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?In the regression modelY = β0 + β1X1 + β2X2 + εthe extent of any multi collinearity can be evaluated by finding the correlation between X1 and X2 in the sample. Explain why this is so.