Inference for the Slope

Is the relationship real?

12 problems · about 22 minutes · VAR-7.J, DAT-3.K

NameDate

Figure — use these to answer the problems

Set the slope to zero. That flat line is exactly what the null hypothesis claims.

y = x + 2

Slope1

y-intercept2

Figure 1

Straightforward practice. Get the method working first.

5 problems

Slope 3.0 with standard error 0.5. What is t?
Answer
2
Why are the degrees of freedom n − 2?
- Two parameters were estimated: the slope and the intercept.
- Because the data comes in pairs.
Slope 1.5, standard error 0.5. What is t?
Answer
A regression on 30 points. Degrees of freedom?
Answer
What value does the null hypothesis give the slope?
Answer

The same ideas with more to keep track of.

3 problems

Slope 0.8, standard error 0.4. What is t?
Answer
A slope interval runs from 0.4 to 2.1. Is a non-zero slope established? 1 yes, 0 no.
Answer
Does a significant slope prove causation? 1 yes, 0 no.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Put the slope inference procedure in order.
Write 1 to 4 in the boxes to put these in order.
- State the null that the population slope is zero.
- Check the conditions, including the residual plot.
- Compute t as the slope over its standard error.
- Use n minus 2 degrees of freedom and conclude in context.
A regression on 50 points. Degrees of freedom?
Answer
The Statistic
Slope 2.4 with standard error 0.6. What is t?
Answer
The Degrees of Freedom
A regression on 22 points. What are the degrees of freedom?
Answer