Inferences 10-3

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

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 = 0 HA: ρ > 0, ρ < 0, ρ ≠ 0 2. Compute the test statistic d.f. = n – 2 Logic dictates how many data sets (n)?

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 = 0 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.

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

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.

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

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