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Lab 7 - Regression, Predictions and Non-linear models

# Lab 7 - Regression, Predictions and Non-linear models - Lab...

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Lab 7: Regression Topics: Confidence Intervals, Plots and Non-Linear Models Objectives: We now assume that the mean of our dependent variable changes as the independent variable changes: 01 [] t t EYX X ββ =+ . The primary objectives for this lab are to: (1) calculate point estimates or predictions for this “population value;” and (2) to create confidence intervals for this “population value” at each level of X. We can create these intervals in Excel using regression results and the formula provided below. This will give us more practice manipulating data in Excel. Minitab actually provides the confidence intervals for us – a good way to check our work. We’ll then consider a simple non-linear model that we can estimate using simple regression and learn about interpreting the results of that model. Key Terms: 1. Regression. 2. Confidence Intervals. 3. Forecasting and Forecast Intervals. 4. Non-Linear Models. Data : Lab 7 – Regression, Forecasting and Growth Models.xlsx Exercises: Real Interest Rate . 1. Open the spreadsheet du jour . Start with the Real Interest Rate worksheet. Estimate a regression model relating interest rates to inflation. Let’s use some different names (X and Y are boring): tt t R Iu β + ; where R t is the T-Bills interest rate (our “ Y variable”) and I t is the rate of inflation (our “ X variable”). You’ll need to create % inflation rates using the CPI. Inflation is the percentage change in the CPI, the following formula can be used to calculate the percentage rate of inflation: 1 1 () 100 t t CPI CPI I CPI =⋅ . 2. Use the Regression tool ( Data , Data Analysis , Regression ) to estimate the regression model relating interest rates to the inflation rate. Include a few of the following options available in Excel’s regression tool: ± Line Fit Plot: The line fit plot is just a plot of the dependent variable ( R t ) against the independent variable ( I t ) with the fitted or predicted values for the dependent variable ( l t R ) included. (Excel gives a funky bar graph – change the chart type to Scatter .) Excel won’t put a line in the graph unless you ask for it. Right-click on one of the markers for the predicted values and then choose Add Trendline . ± Residual Plot: The residual plot is a graph of the errors versus the independent variable. Three of the CRM assumptions were related to the disturbances and these errors are our best guesses about the disturbances. Errors should be distributed fairly evenly around the horizontal axis. The amount of variation should not appear to increase as the independent variable increases and there should not be a discernable pattern as the independent variable changes.

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Lab 7 - Regression, Predictions and Non-linear models - Lab...

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