Consider the following information about variable X: Mean = 4, standard deviation = 2.
Consider the following information about variable Y: Mean = 5, standard deviation = 3.
If there is a correlation of r = 0.52 between variable X and variable Y, what is the intercept for a simple linear regression equation predicting Y on the basis of X? Please provide your answer as a raw score (not a z score) with a minimum of two decimal places.
Solution:
Given:
variable X: Mean = 4, standard deviation = 2
, sx = 2
variable Y: Mean =5, standard deviation = 3
, sy = 3
a correlation of r = 0.52 between variable X and variable Y.
We have to find the intercept for a simple linear regression equation predicting Y on the basis of X.
where
Thus
Thus the intercept for a simple linear regression equation predicting Y on the basis of X is: b0 = 1.88
Consider the following information about variable X: Mean = 4, standard deviation = 2. Consider the...
Given a correlation coefficient (r) of 0.7216, mean of x-bar = 140.5, standard deviation of x (sx) = 6.4, mean of y-bar = 128.3, and standard deviation of y (sy) = 8.2. Find the slope of the regression line. Find the y-intercept of the line. Write the equation of the line.
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) = .8, find Cov(2x-Y, X + 5Y). If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) =...
Random variable X has mean Ux=24 and standard deviation σx =6. Randon variable Y has mean Uy =14 and standard deviation σY = 4. A new random variable Z was formed, where Z=X+Y. What can we conclude about X, Y, and Z with certainty? That is, which one is true?
Suppose x is a normal random variable with mean u and standard deviation o. If z is the standardized normal random variable of x, which of the following statements is false? (1) When r = y, the value of z=0. (2) When z is less than the mean y, the value of z is negative. (3) When r is greater than the mean y, the value of z is positive. (4) It is always the case that z <I.
Given that the correlation between X and Y is 0.84 Mean and standard deviation of X = 4.3 and 3.8 Mean and the standard deviation of Y = 2.7 and 5.6 Find the y-intercept for the line of best fit.
Question 3: Consider the Standard Normal Distribution with mean 0 and standard deviation 1. Find the following. a) P (z>0.5) b) P(z 1.5) c) P (-0.49 < z1.5) Question 4: If you have a normal distribution with mean 14 and standard deviation of 2. What is P(x >16)? Question 5 Professor Hardy assumes the exam scores are normally distributed and wants to grade "on a curve." The mean score was 68, with a standard deviation of 9, If he wants...
2. Suppose that the normally distributed random variable X has mean and standard deviation a. Calculate the z-score of the value x=36. b. Calculate the value that corresponds to a Z-score of a)x= 36 22 b)2=-24 -
Consider the following example of a simple linear regression in R. x = c(-1,0,1) y = c(0,4,2) lm(y"x) ## Call: ## lm(formula = y ~ x) ## Coefficients: # (Intercept) 2 Please write down the design matrix X and compute the values of the slope in the R output (make sure you show the details). Please interpret both intercept and slope in the simple linear regression
1. Identify the formula for predicting an individual's z score on the dependent variable from their z score on the independent variable. a.) (rxy)(zy) b.) (rxy)(zx) c.) zx/zy d.) (zx)(zy) 2. Data from the 1993 World Almanac and Book of Facts were used to predict the life expectancy for men in a country from the life expectancy of women in that country. The resulting regression equation was Yˆ = 9.32 + 0.79(X). Using the regression equation, what would you predict...
Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data322.dat. Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Use the same five numbers to find the equation of the regression line for predicting the time an icicle has been growing from its length. Round your answers to three decimal places time length 10...