501_Lecture_10

# 501_Lecture_10 - Section 10.1 Simple Linear Regression A...

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Unformatted text preview: Section 10.1 Simple Linear Regression A continuation of Chapter 2 Statistical model for linear regression Data for simple linear regression Estimation of the parameters Confidence intervals and significance tests Confidence intervals for mean response vs. Prediction intervals (for future observation) Example: We observe 92 males aged 20 to 29. We measure skin-fold thickness and body density. Part of the data: ID Iskin Den 1 1.27 1.093 2 1.56 1.063 3 1.45 1.078 4 1.52 1.056 5 1.51 1.073 … The scatterplot with the LSR line: SAS output for the data We will often be using software for calculations in this section. SAS output for the data: We can use: proc reg see file named Regression 2 . This program has more tools than the regression.doc file (studied in Chapter 2). Settings of Simple Linear Regression Now we will think of the least squares regression line computed from the sample as an estimate of the true regression line for the population. Different Notations than Ch. 2. Think b 0 = a, b 1 = b (from data) The statistical model for simple linear regression: Data: n observations in the form (x 1 , y 1 ), (x 2 , y 2 ), … (x n , y n ). The deviations ε i are assumed to be independent and N(0, σ )....
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501_Lecture_10 - Section 10.1 Simple Linear Regression A...

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