# EconHM22 - Question#1 Based on this data on the...

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Question #1 Based on this data on the experience (in years) and salary (in thousands of dollars) of 51 employees of a firm, answer the following questions using your results of the sample linear regression of salary (dependent variable) on experience (independent variable) and the corresponding residual plot. 1. The scatterplot of salary on experience suggests that there is A positive curve- linear relationship between salary and experience. 2. Which one of the following seems to be an accurate representation of the residual plot. An U-shaped band. 3. The residual plots of regressing experience (dependent variable) on salary (independent variable) will be the opposite of the residual plot from a regression of salary on experience and exhibit an inverted-U shape band. 4. The value of R?you obtain from this regression is 0.784507379 = 0.784507379 5. Now add an additional independent variable, called "experience2". Create this variable by squaring all the values of experience and entering them in to a new column. Now run a multiple regression with experience and experience2 as your independent variables, keeping salary as your dependent variable. (This is defining a curvilinear relationship between salary and experience.) In this case, the value for R?is 0.963849893 Question #2 A general manager at a supermarket chain believes that sales of a product are influenced by the amount of space the product is alloted on shelves. If true, this would have great significance, because the more profitable items could be given more shelf space. The manager realizes that sales volume would likely increase with more space up to a certain point. Beyond that point, sales would likely flatten and perhaps decrease (because customers often are dismayed by very large exhibits). To test his belief, the manager records the number of boxes of detergent sold during 1 week in 25 stores in the chain. For each store, he records the shelf space (in inches) alloted to the detergent. The data is stored here . 1. The scatterplot of SALES on SPACE suggests that there is a negative curve- linear relationship between SALES and SPACE. 2. Run a regression with SALES as your dependent variable and SPACE as your independent variable. The adjusted R 2 is -0.015210895 , while the p-value

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for the overall F-test is 0.431751675 , indicating that at the 5% level of significance, the linear model is not valid . 3. Now, since the inital scatterplot suggested a non-linear relationship between SALES and SPACE, it was expected that the linear model would not be a good fit. Now create an additional independent variable calles SPACE2, which is going to take squared values of the SPACE column and run a regression with two independent variables (SPACE and SPACE2). The adjusted R 2 is 0.352828885 , while the p-value for the overall F-test is 0.003202847 , indicating that at the 5% leve of significance, the quadratic model is valid . Looking at the two independent variables, you can say that at the 10% level of
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## This note was uploaded on 02/11/2010 for the course ECON 203 taught by Professor Petry during the Spring '09 term at University of Illinois, Urbana Champaign.

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EconHM22 - Question#1 Based on this data on the...

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