AP Statistics : How to test of significance for the slope of a least-squares regression line
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Example Question #1 : How To Test Of Significance For The Slope Of A Least Squares Regression Line
A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.
True
False
True
A p-value of 0.1 is generally not sufficient to reject the null hypothesis, but this is only because we want a high degree of confidence before finding a relationship between variables. Here, there is most likely a relationship between the variables even though the statistician could not reject the null hypothesis.
Example Question #1 : How To Test Of Significance For The Slope Of A Least Squares Regression Line
For a data set, the least-squares regression line has a 
Based on this confidence interval, what can you do with a hypothesis test at 
Fail to reject the null hypothesis because this confidence interval does not include 
Reject the null hypothesis because this confidence interval does not include 
Reject the null hypothesis because this confidence interval does not include 
Fail to reject the null hypothesis because this confidence interval does not include 
Not enough information to be able to decide.
Reject the null hypothesis because this confidence interval does not include
Notice that the interval does not include 
Any confidence interval can be used to create a hypothesis test by inverting it, and it is fairly simple, but the concept is tested into graduate-level statistics theory.
Example Question #1 : How To Test Of Significance For The Slope Of A Least Squares Regression Line
Which of the following is an incorrect condition requirement for regression inference?
Ordered pairs must be independent of each other
Response must vary normally about the regression line for any given value of
A linear relationship between 
A trend/pattern of some sort in the residual plot
The standard deviation of the response must be constan
A trend/pattern of some sort in the residual plot
All of the following choices are correct conditions except for the choice concerning a trend/pattern of some sort in the residual plot. For regression inference to be accurate, we need to look at the residual plot of the data of interest and make sure there is random scatter. Random scatter indicates that the ordered pairs are indeed independent of each other. Any sort of pattern present in the residual plot would not satisfy that requirement, and therefore would not enable us to successfully use regression inference.
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