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Lab 3 Scatter Diagrams, Covariance, Correlation and Regression

# Lab 3 Scatter Diagrams, Covariance, Correlation and Regression

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Lab 3: The Sampling Distribution, Interval Estimation, Correlation and Covariance Objectives: 1. Still more practice with Excel: equations and functions. 2. Bivariate distributions – relationship between two variables. 3. Introduce the concepts of covariance and correlation – variables that are related to each other. 4. Descriptive measures of covariance and correlation. Key Terms: 1. Scatter Diagrams / X-Y Graphs. 2. Covariance and correlation . Data : Your Excel file from Lab 2, which continues our use of the Excel file: AmherstHomeSales2006 .xlsx . And an additional data set on home prices in Belchertown and Amherst. Exercises: Two-Sample Hypothesis Test of Means 1. The question we ask is: ‘Are the population mean house prices the same in Amherst and Belchertown?’ Thus, our hypothesis can be stated: H 0 : μ A = μ B ; H A : μ A μ B . 2. If the sample means for both Amherst and Belchertown homes are normally distributed (CLT here), then the difference is also normal, and we an apply the Z-test, or t-test if we don’t know the true standard deviations. 3. We presume no knowledge of the true population standard deviations. Thus, our safest choice for test statistics is a formulation that assumes unequal variances: ( ) ( ) 1 2 1 2 2 2 1 2 1 2 calc X X t s s n n μ μ = + , the degrees of freedom calculation for this statistic is a bit involved and will fall somewhere between the sample sizes for the two samples. Luckily, as we’ll see, Excel takes care of this for us. 4. We could easily calculate that in Excel, but if we go to Data and Data Analysis , we’ll find t-test: Two-Sample Assuming Unequal Variances . Click OK. The next window asks for the data range for each of the “two variables.” Here, we’ll treat the Amherst prices and Belchertown prices as different variables. Whoa! What do we need to do first before trying this test?? 5. Right, once you’ve done that, highlight the Amherst prices for Variable 1 and the Belchertown prices for Variable 2. What is the Hypothesized Mean Difference ? You also get to choose α . Then select the Output Range : a cell with lots of space below and to the right. Now click OK and

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