Question

Topic regression analyses:

Please calculate the following from the data posted in excel. Let the inflation rate be the Y variable and the unemployment rate be the X variable. Please do this in excel unless otherwise noted in the question.

A bit of context for the problem, the relationship between the inflation rate and unemployment rate is called the Philips curve in economics. The relationship is Yinflation rate=MXunemployment rate+ei this is used to estimate what the federal reserve’s policies should be in the upcoming year to minimize inflation. The data for the relationship is:

Inflation	Unemployment
2%	10%
3%	6%
6%	3%
10%	2%
1%	15%
15%	1%
5%	4%

Recall the regression line is the following (Y=Mx+B)

1. The relationship between the X variable and the Y variable (m)
2. Please calculate the constant of the regression line (B)
3. What does the e represent in the model? Please give a simple explanation.
4. Use the model to predict what inflation would be if the unemployment rate was 12%?, 20%?
5. Do the estimates of the model accurately reflect the observed inflation rate? If not please give a simple explanation as why not.
6. What Is the R^2 of the model? What does this represent?

Answer 1

We need to do the regression in excel. Setting up the table as shown

Performing regression by the steps

Click on Data -> Data analysis -> Regression. A window will open

Clicking OK, we get the regression output as follows

So, after the regression, the relationship is

• Y (Inflation rate) = -0.795X+0.1066
• Since the slope is negative, -0.795, the relationship is negative
• Constant of the line, B is 0.1066
• e represents the error in predicting the value of y for a given x. Error is created when the regression model does not predict the values 100% accurate.
• If the unemployment rate was 12%, the inflation would be Y = -0.795*0.12+0.1066 = 0.011136. So for 12% unemployment, inflation rate is 1.1136%
• If the unemployment rate was 20%, the inflation would be Y = -0.795*0.2+0.1066 = -0.0525. So for 20% unemployment, inflation rate is -5.25%
• The model is valid as the p-value for coefficient is very small. Though the model is not representing the actual observed rate, it is very close to that. The predicted values are as shown for the observed values using this regression model. The SSE is also not high. So it is good estimate

• R2 is 64.5%.This represent that 64.5% variability in inflation rate is explained by the unemployment rate

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