A simple linear regression of Y on X reveals that the slope b is 3; the standard deviation of X is 2; and the standard deviation of Y is 8. What is the correlation coefficient between X and Y? Show steps.
The slope (b) can be calculated as follows:
b = r sY/sX
We can find 'r' from here
3 = r * 8/2
r = 0.75
A simple linear regression of Y on X reveals that the slope b is 3; the...
please help! Following is a simple linear regression model: y = a + A + & The following results were obtained from some statistical software. R2 = 0.523 Syx (regression standard error) = 3.028 n (total observations) = 41 Significance level = 0.05 = 5% Variable Interecpt Slope of X Parameter Estimate 0.519 -0.707 Std. Err. of Parameter Est 0.132 0.239 Note: For all the calculated numbers, keep three decimals. Write the fitted model (5 points) 2. Make a prediction...
Qm250 The slope of Regression line is 3 14 In simple regression, if x and y are directly related and i " and the predicted (estimated) y value corresponding to the slope (estimated) y value corresponding to x- 10 is 50 the regression line w , find the the regression line b. 60 ?.10 a. 4.7 15. Which of the following statements is not true ab cance level is divided equally between the 2 tails of the a. The signifi...
True or false?: 1) If X and Y are standardized, then fit a linear regression line of standardized Y on standardized X, correlation between X and Y equals the slope of regression line. 2) If one calculates r for a set of numbers and then adds a constant to each value of one of the variables, the correlation will change. 3) The easiest way to determine if a relationship is linear is to calculate the regression line. 4) If the...
In the simple linear regression model, the slope represents the: A. change in y per unit change in x B. value of y when x = 0 c. change in x per unit change in y D. value of x when y = 0 In the first-order linear regression model, the population parameters of the y-intercept and the slope are estimated by CA. bo and A CB. bo and b CC. A and Po CD. b and Bo
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
True or false: 1) If X and Y are standardized, then fit a linear regression line of standardized Y on standardized X, correlation between X and Y equals the slope of regression line. 2) If one calculates r for a set of numbers and then adds a constant to each value of one of the variables, the correlation will change. 3) The easiest way to determine if a relationship is linear is to calculate the regression line. 4) If the...
Q5). Show that in a simple linear regression Σεί 0 (a). (). (X,Y) is a point on the fitted regression line. (d). Verify parts (a), (b), and (c) for the data in the folder "Regression and Correlation" at the course blackboard site. You are free to use software or calculator for the verification. Q5). Show that in a simple linear regression Σεί 0 (a). (). (X,Y) is a point on the fitted regression line. (d). Verify parts (a), (b), and...
If the slope of regression line is b1 = 0.1, standard deviation of x = 24 and correlation coefficient r= 0.8, what will be the value of standard deviation of y? 6342
2. Show that R-squared (for a simple linear regression) is equal to the square of the correlation between y and r. (Hint: Use one of the R-sqared formulas and plug in the formula for the slope estimator.)