1. Inferences
10-3

2. What about making inferences?
r, a and b are the sample test statistics
Sample r becomes population ρ
and ŷ = ax + b becomes y = αx + β
Certain assumptions must be met:
(x,y) is a random sample from the population
For each fixed x, the y has a normal distributions.
All the y distributions have the same variance
CHECK BVD

3. Testing ρ 2. Compute the test statistic
i.e. Testing whether there is or is not a linear correlation
1. Set your hypotheses
HO: ρ = HA: ρ > 0, ρ < 0, ρ ≠ 0
2. Compute the test statistic
d.f. = n – 2
Logic dictates how many data sets (n)?

4. Testing ρ 2. Compute the test statistic 3. Find the P-value
i.e. Testing whether there is or is not a linear correlation
1. Set your hypotheses
HO: ρ = HA: ρ > 0, ρ < 0, ρ ≠ 0
2. Compute the test statistic
3. Find the P-value
4. Compare to α and conclude.
5. State your conclusion.

5. Measuring Spread Error can be determined a number of ways
Method 1: Using residual
Where ŷ = ax + b, and n > 3
Use this one!!

6. Measuring Spread (cont)
Method 2: a confidence interval for y
True y, for a population, has a population slope, a population y intercept, plus some sort of random error.
Therefore, we can create a confidence interval for y that allows us to predict true y.

7. Measuring Spread (cont)
Method 2: This will look familiar…. Based on n ≥ 3 data pairs, after finding ŷ use
Where ŷ = ax + b, c = confidence level, n = number of data pairs, and Se is the standard error of estimate

9. Least Squares Line Equation of a line: y = mx + b
In statistics: ŷ = a + bx (Our book)
also: ŷ = b0 + b1x
There are formulas for a and b