Simple Linear Regression
Stat 326 – Introduction to Business Statistics II
Review – Stat 226
Spring 2013
Stat 326 (Spring 2013)
Introduction to Business Statistics II
1 / 47
Stat 326 (Spring 2013)
Introduction to Business Statistics II
2 / 47
Review: Inference for Regression
Example: Real Estate, Tampa Palms, Florida Goal: Predict sale price of residential property based on the appraised value of the property Data: sale price and total appraised value of 92 residential properties in Tampa Palms, Florida
1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars)
Review: Inference for Regression
We can describe the relationship between x and y using a simple linear regression model of the form µy = β 0 + β1 x
1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars)
response variable y : sale price explanatory variable x: appraised value relationship between x and y : linear strong positive
We can estimate the simple linear regression model using Least Squares (LS) yielding the following LS regression line: y = 20.94 + 1.069x
Stat 326 (Spring 2013)
Introduction to Business Statistics II
3 / 47
Stat 326 (Spring 2013)
Introduction to Business Statistics II
4 / 47
Review: Inference for Regression
Interpretation of estimated intercept b0 : corresponds to the predicted value of y , i.e. y , when x = 0
Review: Inference for Regression
Interpretation of estimated slope b1 : corresponds to the change in y for a unit increase in x: when x increases by 1 unit y will increase by the value of b1
interpretation of b0 is not always meaningful (when x cannot take values close to or equal to zero) here b0 = 20.94: when a property is appraised at zero value the predicted sales price is $20,940 — meaningful?!
Stat 326 (Spring 2013)
Review – Stat 226
Spring 2013
Stat 326 (Spring 2013)
Introduction to Business Statistics II
1 / 47
Stat 326 (Spring 2013)
Introduction to Business Statistics II
2 / 47
Review: Inference for Regression
Example: Real Estate, Tampa Palms, Florida Goal: Predict sale price of residential property based on the appraised value of the property Data: sale price and total appraised value of 92 residential properties in Tampa Palms, Florida
1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars)
Review: Inference for Regression
We can describe the relationship between x and y using a simple linear regression model of the form µy = β 0 + β1 x
1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars)
response variable y : sale price explanatory variable x: appraised value relationship between x and y : linear strong positive
We can estimate the simple linear regression model using Least Squares (LS) yielding the following LS regression line: y = 20.94 + 1.069x
Stat 326 (Spring 2013)
Introduction to Business Statistics II
3 / 47
Stat 326 (Spring 2013)
Introduction to Business Statistics II
4 / 47
Review: Inference for Regression
Interpretation of estimated intercept b0 : corresponds to the predicted value of y , i.e. y , when x = 0
Review: Inference for Regression
Interpretation of estimated slope b1 : corresponds to the change in y for a unit increase in x: when x increases by 1 unit y will increase by the value of b1
interpretation of b0 is not always meaningful (when x cannot take values close to or equal to zero) here b0 = 20.94: when a property is appraised at zero value the predicted sales price is $20,940 — meaningful?!
Stat 326 (Spring 2013)