Consider the following simple linear regression model: y = ?0 + ?1x + ?. When determining whether x significantly influences y, the null hypothesis takes the form ________. H0:b1 = 1 H0:?1 = 1 H0:?1 = 0 H0:b1 = 0
As the coefficient of X in the equation is and we are trying to test the significance of the independent variable X in the equation, therefore the null and the alternate hypothesis here would be given as:
Consider the following simple linear regression model: y = ?0 + ?1x + ?. When determining...
Consider the simple linear regression model: Suppose that the estimate of B1 based on a sample of 55 individuals is 2.3 and the corresponding standard error is 0.96. Test the null hypothesis H0: β1-0 vs HA: A 0 at the α-0.05 level and provide the corresponding p-value.
Q. 20 In a simple linear regression, when testing H0: β1 = 0, against H1: β1 ≠0, failing to reject the null hypothesis means that: a. the slope of the regression line is not zero b. the relationship between x and y may be multiplicative c. there is no linear relationship between x and y d. there is a linear relationship between x and y e. None of the above
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...
In a simple linear regression model, the intercept term is the mean value of y when x equals _____. a. y b. −1 c. 1 d. 0
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Consider the following simple linear regression model: y=Po+P1x Po and B1 are Multiple Choice 41 the response variables the random error terms the unknown parameters the explanatory variables 11 of 30 Prev Next
Econometrics 13) Consider the classical linear regression model y = XB + E, EN(0,021) The data are collected in such a way that the X matrix is orthogonal, that is X'X = 1. We want to test the null hypothesis that Ho: B1 + B2 + ... + Bx = 0. For this particular hypothesis, the standard t-test for a single linear restriction r' B = q reduces to ki bi a) t= i=1 b) t = svk Ek=1b c)t...
2. Suppose we observe the pairs (X, Y), i-1, , n and fit the simple linear regression (SLR) model Consider the test H0 : β,-0 vs. Ha : Aメ0. (a) What is the full model? Write the appropriate matrices Y and X. (b) What is the full model SSE? (c) What is the reduced model? Write the appropriate matrix XR. (d) What is the reduced model SSE? (e) Simplify the F statistics of the ANOVA test of Ho B10 vs....
(Do this problem without using R) Consider the simple linear regression model y =β0 + β1x + ε, where the errors are independent and normally distributed, with mean zero and constant variance σ2. Suppose we observe 4 observations x = (1, 1, −1, −1) and y = (5, 3, 4, 0). (a) Fit the simple linear regression model to this data and report the fitted regression line. (b) Carry out a test of hypotheses using α = 0.05 to determine...