<p> Statistics 103 Probability and Statistical Inference Instructions for lab 8</p><p>Lab Objective </p><p>Practice with simple linear regression and correlation</p><p>Lab Procedures</p><p>Long-term interest rates drive much of the economic activity in the U.S. When interest rates are low, people and establishments are more likely to borrow money for purchasing homes or growing their businesses. When interest rates are high, people and establishments are less likely to do so. In this lab, we'll work with economic data from the U.S. from 1980 to 1998 to explore relationships involving interest rates.</p><p>Open the data file USeconstat.JMP. The data are culled from the 1997 Organization for Economic Cooperation and Development economic outlook report. There are dozens of variables, but we'll only use a small number. For convenience, all the relevant variables are among the first few columns in the JMP file.</p><p>Questions</p><p>1. How did long-term interest rates change annually between 1980 - 1998? Were they (i) generally going up; (ii) generally steady; (iii) generally going down; or (iv) all over the place? Just write a short phrase as your answer. </p><p>2. Using the data, describe the relationship between long-term interest rates and unemployment rates. Include in your descriptions a one-number summary of the strength of the association between the two variables. </p><p>3. Using the data, describe the relationship between long-term interest rates and gross domestic product (market prices). Include in your descriptions a one-number summary of the strength of the association between the two variables. </p><p>4. We wish to model the relation between unemployment rate (response) and long-term interest rate (predictor) using a simple linear regression model. </p><p> a. Write down the linear model and the estimated model coefficients (intercept, slope, and residual variance). b. Interpret the intercept coefficient. c. Interpret the slope coefficient. d. Interpret the residual variance. e. Construct a 95% confidence interval for the association between long-term interest rate and unemployment rate. f. Perform a two-sided hypothesis test with the null hypothesis that the slope is zero at a significant level of 0.05. What is your conclusion? g. What is the r2 value? </p><p>5. Now fit a linear model between gross domestic product (response) and long-term interest rate (predictor) using a simple linear regression model. a. What is the r2. Under a linear model, does long-term interest rate capture the variation in gross domestic product better than unemployment rate? b. Click the red down arrow next to Linear Fit and pull to Confid Shaded Fit. This plots the 95% confidence interval for the mean value of y for a given value of x for all values of x. This shaded area is constructed based on the sampling distribution of the intercept and the slope. b.i. How many observations lie outside of this confidence region? b.ii. Note how the confidence interval tends to be wider at the ends! Why is this? c. Click the red down arrow next to Linear Fit and pull to Confid Shaded Indiv. This plots the 95% prediction interval of y for a given value of x for all values of x. How many observations (what percentage) lie outside of this confidence region? Why is this shaded area larger? </p>