STAT1008 Lecture Notes - Lecture 9: Confidence Interval, Standard Deviation, Scatter Plot
9.1 INFERENCE FOR SLOPE AND CORRELATION
Outline
- Simple Linear Model
- Inference for the slope
o CI for slope
o Test for slope
o Test for correlation
o Coefficient of determination, R2
o Checking conditions
Recall: Lease Square Regression
Simple Linear Model
- The population/true simple linear model is
- b0 and b1 are unknown parameters → try to estimate from some sample
- Estimate with the least squares line
- How accurate are the estimates?
Inference for the Slope
- Confidence intervals and hypothesis tests for the slope can be done using the familiar formulas:
- But how do we estimate the standard error?
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o Bootstrap/Randomization distributions?
o Computer output
Technology Examples
Intercept = b0
Chirps = b1
1.63e-05 = 1.63 x 10 power negative 5
Confidence Interval for Slope
- B1 and SE come from computer output
- T* uses n-2 degrees of freedom
Technology Examples
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find more resources at oneclass.com
Test for Slope
Test for Correlation
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find more resources at oneclass.com
Document Summary
Inference for the slope: ci for slope, test for slope, test for correlation, coefficient of determination, r2, checking conditions. B0 and b1 are unknown parameters try to estimate from some sample. Confidence intervals and hypothesis tests for the slope can be done using the familiar formulas: But how do we estimate the standard error: bootstrap/randomization distributions, computer output. 1. 63e-05 = 1. 63 x 10 power negative 5. B1 and se come from computer output. Recall that for correlation: -(cid:1005) r (cid:1005) If we square the correlation, r2, we get a number between 0 and 1 that can be interpreted as a percentage. = proportion of variability i(cid:374) respo(cid:374)se (cid:448)aria(cid:271)le y that is (cid:862)e(cid:454)plai(cid:374)ed(cid:863) (cid:271)(cid:455) the (cid:373)odel (cid:271)ased o(cid:374) the (by convention we use a capital , although the value is just for a single predictor) 98. 13% of the variability in these temperatures can be explained by the cricket chirp rates. predictor x.
