This problem involves simple linear regression without an intercept. (a) Recall that the coefficient estimate ˆ...
This problem involves simple linear regression without an intercept.
(a) Recall that the coefficient estimate ˆ β for the linear regression of Y onto X without an intercept is given by (3.38). Under what circumstance is the coefficient estimate for the regression of X onto Y the same as the coefficient estimate for the regression of Y onto X?
(b) Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is different from the coefficient estimate for the regression of Y onto X.
(c) Generate an example in R with n = 100 observations in which
the coefficient estimate for the regression of X onto Y is the same
as the coefficient estimate for the regression of Y onto X.
Homework Answers
Under what circumstance is the coefficient estimate for the regression of X onto Y the same as the coefficient estimate for the regression of Y onto X
Var(X) and Var(Y) are equal, which is to say that both X and Y have equal tendency to be away from the mean. They should be the same when the coefficient is 1, and there is no noise, different otherwise.
(b) and (C)
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This problem involves simple linear regression without an
intercept.
(a) Recall that the coefficient estimate ˆ...
Consider the fitted values that result from performing simple linear regression without an intercept, i.e., the...
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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
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...
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