3 min read•june 18, 2024
Josh Argo
Jed Quiaoit
Josh Argo
Jed Quiaoit
Just as we had with other units regarding inference, there was always the and the test inference method. Since sections 9.3 and 9.4 dealt with the prediction method (confidence intervals), we will not tackle the testing methods by testing claims about our population.
Recall that we'll model our slopes using a . Likewise, previous units illustrated that a is a statistical test that is commonly used to determine whether there is a significant difference between the mean of a sample and a hypothesized value. In the context of a regression model, a t-test for the slope can be used to test the of the slope, which represents the relationship between the (also known as the predictor variable) and the . ⛰️
In general, If the t-statistic for the slope is significantly different from zero, it suggests that there is a meaningful relationship between the two variables and that the slope is not equal to zero. On the other hand, if the t-statistic is not significantly different from zero, it suggests that there is not a strong relationship between the variables and that the slope is likely equal to zero.
The first thing we need to make sure is clear before we perform our test is to set up our null and alternate hypotheses. Since we are performing hypothesis tests on the slope of a regression model, our null and will look as according:
For example, an Easter candy researcher may claim that the between the number of jelly beans consumed per day and the amount of Easter grass cluttering the house has a slope of 40 ("As the jelly bean consumption increases by 1, the number of easter grass pieces is predicted to increase by 40"). 🐰
If this were the test, you would test it using these hypotheses:
Just like our other hypothesis tests, we have conditions for the inference that must be met. For hypothesis tests for slope, here are the four necessary conditions: 4️⃣
The test you will run in this instance is a . In most graphing calculators, this is known as LinRegTTest under the Stats>Tests menu. 📝
Since we are dealing with quantitative data and it is unlikely we know the population standard deviation of y, we must use a t distribution for our critical value.
Let’s go! You have now verified the conditions to be met, wrote your hypotheses and identified the correct test, so we can calculate now! ❤️
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