An economic policy research organization has asked you to...

An economic policy research organization has asked you to study the relationship between disposable income and unemployment level. The data for this study are contained in the data file Economic Activity. As a first step you estimate the regression model for the relationship between unemployment regressed on disposable income. Determine if there is a significant relationship between unemployment and disposable income and whether the relationship is increasing or decreasing. Compute the $95 \%$ prediction interval for unemployment when disposable income is $$\$ 30,000$$.

An economic policy research organization has asked you to study the relationship between disposable income and unemployment level. The data for
this study are contained in the data file Economic Activity. As a first step you estimate the regression model for the relationship between unemployment regressed on disposable income. Determine if there is a significant relationship between unemployment and disposable income and whether the relationship is increasing or decreasing. Compute the $95 \%$ prediction interval for unemployment when disposable income is $$\$ 30,000$$.

Key Concepts

Direction of Relationship

Interpreting the sign of the regression coefficient is critical to understanding whether the relationship is increasing or decreasing. A positive coefficient indicates that as the independent variable increases, the dependent variable tends to increase, while a negative coefficient implies a decreasing relationship.

Prediction Interval

A prediction interval provides a range in which a new observation is expected to fall, with a specified level of confidence (such as 95%). It accounts for the uncertainty in the regression estimates as well as the inherent variability in the data, making it broader than a confidence interval for the mean response.

Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It provides estimates of parameters, such as the slope and intercept, which help to understand how changes in the independent variable are associated with changes in the dependent variable.

Hypothesis Testing in Regression

This concept involves testing whether the relationship between the variables, captured by the regression coefficient (slope), is statistically significant. It typically involves setting up null and alternative hypotheses about the parameter values and using t-tests to decide if the observed coefficient is significantly different from zero.

Transcript

00:01 Part 1.

00:04 This is the estimated auto -regression first order model.

00:13 We regress unemployment with its first lag.

00:21 And we will use this estimated equation to predict the value of unemployment rate in 2004, given the unemployment rate in 2003.

00:37 In 2003, the unemployment rate was 6.

00:45 So if you plug 6 in here, you will get unemployment rate in 2004 as 5 .94.

01:05 From the 2005 economic report of the president, table b -42, the us civilian unemployment rate was 5 .5.

01:24 So the equation here over predicts the 2004 unemployment rate by almost half a percentage point.

01:55 In part 2, we add inflation of the previous period into the right -hand side of the equation.

02:11 We find that the lag inflation is very statistically significant.

02:17 It has a high t statistic value, which is about 4 .7.

02:54 Part 3.

02:55 We use the equation from part 2 to predict unemployment rate in 2004.

03:03 Again, we know that unemployment rate in 2003 is 6, and from their data set, we know inflation rate in 2003 was 2 .3.

03:19 Plug these numbers into the estimated equation here.

03:28 You will get unemployment in 2004 as 5 .61.

03:39 It is still larger than the actual unemployment rate of 5 .5, but it is much closer to the real rate, comparing to our prediction in part 1.

03:58 We get 5 .94 in part one.

04:08 In part four, we will construct a 95 % confidence interval for our predicted unemployment rate.

04:25 We will assume that unemployment follows a conditional normal distribution.

04:33 And to construct the confidence interval, we need centered error of predicted value, which i denote as e of y0...

Please give Ace some feedback