How to test of significance for the slope of a least-squares regression line - AP Statistics
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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.
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.
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.
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.
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Which of the following is an incorrect condition requirement for regression inference?
Which of the following is an incorrect condition requirement for regression inference?
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.
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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For a data set, the least-squares regression line has a 
confidence interval for the slope of 
.
Based on this confidence interval, what can you do with a hypothesis test at 
significance level where 
and 
?
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
Notice that the interval does not include 
. This means that the P-value for the hypothesis test would be under 5%, which would lead us to reject our null hypothesis.
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.
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.
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