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7 Cards in this Set
- Front
- Back
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Linear Equation |
Y= mX + b Y= dependent variable X= independent variable m = slope (tells us about the direction of relationship) b = intercept |
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Linear equation lets us perform the following tasks: |
-summarize the relationship among variables by an equation -make predictions on a variable based on data for related variables (Thing 1) -Measure the sensitivity of one variable to changes in a related variable (Thing 2) |
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Regression equation |
Ŷ= b0+ b1X - Ŷ = dependent variable, or response or predicted variable - X is the independent variable, or predictor or explanatory variable - Simple regression, only 1 predictor variable (X). - In multiple regression, 2 or more X, denoted as:X1, X2, X3, …, Xn - b0 is the intercept of the regression line - b1 is the slope of the regression line |
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Prediction and Forecasting Thing 1: Plug and Chug |
- Dep var = intercept + slope * Indep var - Predicted Y = Y-hat = Ŷ= b0+ b1X Given a value for X, plug into the regression equation and chug out the value for Y Example:firstclass mail volume (1stClVol) and population (PopUSA) ¤Predicted (1stClVol) = - 116 + 0.80 * (PopUSA)So, tell me population and I’llpredict or forecast first class mail volume. Example: if population is expectedto be 370: ¤Predicted1stClVol = - 116 + 0.80*(370)= 180 |
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Prediction and Forecasting Thing 2: Marginal Effects |
- Dep var = intercept + slope * Indep var - Predicted Y = Ŷ= b0+ b1X - Given a change in X, the change in Y is the slope times the change in X changein Y = slope * change in X ∆Y= b1* ∆X Example:firstclass mail volume (1stClVol) and population (PopUSA) ¤Predicted (1stClVol) = - 116 + 0.8*(PopUSA)So, tell me the change in populationand I’ll predict the change in first class mail volume. So, if population isexpected to grow by 10 million then mail volume is expected to increase by 8billion: ∆Y= slope*∆X = 0.8*(10)= 8 |
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Time Series Special Case: |
When time itself is the independent variable in the simple regression analysis, the equation is: Predicted Y = Ŷ= b0 + b1 Time Time trends: upward, downward or no trend Trend Rates only apply to time trends The trend rate is the coefficient of the time variable, or the slope of the regression equation (b1) |
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Time Series Special Case Example: |
Example of unemployment: Un = Unemployment in percent of thelabor force The regression equation is the timetrend: Ŷ = Predicted Un% = b0 + b1Time Result: Predicted Un% = 10.13 - 0.06Month Thing1: What will unemployment be in six months? Predicted Un% = 10.13 - 0.06*(37) = 7.9% Thing 2: Unemployment falls by 0.06 (b1)percentage pts/month, 0.18 pts/quarter,or 0.72 pts/year |
