Linear Regression Analysis: Fertilizer and Wheat Yield - Prof. The Staff, Study notes of Statistics

Download Linear Regression Analysis: Fertilizer and Wheat Yield - Prof. The Staff and more Study notes Statistics in PDF only on Docsity! STA 100 Lecture 22 Linear Regression and Correlation I. Introduction Simple linear regression is one of the most widely used statistical techniques for developing a mathematical relationship between a dependent variable and an independent variable. A Practical Problem: In an agricultural study we would like to develop a linear relationship between the wheat yield measured in bushels/acre and fertilizer level measured in pound/acre. The following data were collected from seven randomly selected plots: Fertilizer (x) Yield (y) (Pounds/Acre) (Bushels/Acre) 100 40 200 50 300 50 400 70 500 65 600 65 700 80 We are interested in fitting a regression model to the data and using the model for the estimation and prediction. II. The Model a. The simple linear regression model is: y = βo + β1 x + ε b. The Least Squares Estimation: Let y^ = bo + b1 x denote the estimated regression line. Find bo and b1 such that SS(resid) = Σ ( y – y^ )2 is minimized. Wheat Yield 0 10 20 30 40 50 60 70 80 90 0 200 400 600 800 Fertilizer (Pounds/Acre) Example: Wheat yield Fertilizer (x) Yield (y) (Pounds/Acre) (Bushels/Acre) 100 40 200 50 300 50 400 70 500 65 600 65 700 80 2