Hello. Would you please answer my question of four problems? Thank you a million

Question

Hello. Would you please answer my question of four problems?

Thank you a million!

(Statistics) - Simple linear regression

1. True/False:

A) In a simple linear regression model (Y | X) = 0 + 1X, if the null hypothesis H0: 1 = 0 is not rejected (p = 0.32), this means there is no relationship between X and Y.

True or False?

B) Confidence intervals for (Y | X0) are narrowest for values of X0 that are far from the mean value X bar.

True or False?

C) If the estimate of 1 is very large, this means that X and Y are highly correlated.

True or False?

2. Please describe what we mean by 'subpopulation variance'.

3. What assumptions are necessary to produce valid inference for a simple linear regression model?

4. How do you estimate the subpopulation variance 2 in simple linear regression?

Explanation / Answer

For simple linear regression, the chief null hypothesis is H0:1= 0, and the corresponding alternative hypothesis is

H1:1is not equal to 0. If this null hypothesis is true,then, from E(Y) =0+1x we can see that the population mean of Y is 0 for every X value, which tells us that x has no effect on Y.

1)A) true

from this if x is far from mean the interval will be wider but not narrower

b)false

c) we know the formula for correlation coefficient r =1 (sdx/sdy)

as 1 increasese r value increases this results in high correlation between x and y.

2) subpopulation variance is the error variance which indicates how many observations deviate from the fitted surface.

3)Assumptions of Linear Regression

Linear regression is an analysis that assesses whether one or more predictor variables explains the dependent (criterion) variable. The regression has five key assumptions:

4)

.

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