(b) Perform the regression and interpret each of the slopes. (c) Is there a significant difference between sales in the different quarters? (d) According to the model, what is the difference between third and fourth quarter sales? (e) Are there any variables that do not contribute significantly to the model? If so, reduce the model appropriately and repeat parts (b) and (c). Comparing two slopes: p. 622, #12.40 For part (a), they mean an ordinary linear model. Omit (i), (j), (k), (l) since they do not tell us anything interesting. Part (m) refers to the linear model. Also, answer the following question: If we ignore shelf space (notice the nice distribution of shelf sizes anyway) do items placed in front sell better than object placed at the back? Excel Assignment 2 Go the web site at and download the Assignment 2 Excel worksheet. Important: Use the 90% level of significance throughout. Part 1: Extract the Long Island home sales data only. Let y = Sales price in $1000 x 1 = Number of bedrooms x 2 = Time on market in weeks x 3 = Taxes & Maintenance Perform three regressions as follows. In each case, write down the regression model with coefficients rounded to 4 significant digits, and use the model to predict the selling price of a 3-bedroom home whose with $25,000 taxes after 10 weeks on the market. (a) Multiple linear model: y = ∫ 0 + ∫ 1 x 1 + ∫ 2 x 2 + ∫ 3 x 3 (b) Interactive Model: y = ∫ 0 + ∫ 1 x 1 + ∫ 2 x 2 + ∫ 3 x 3 + ∫ 4 x 1 x 2 + ∫ 5 x 1 x 3 + ∫ 6 x 2 x 3 (c) Quadratic model: y = ∫ 0 + ∫ 1 x 1 + ∫ 2 x 2 + ∫ 3 x 3 + ∫ 4 x 1 2 + ∫ 5 x 2 2 + ∫ 6 x 3 2 (d) Full second order model: y = Quadratic model + interactive terms
61 (e) Compare the model in (d) with those in (b) and (c). Based on the outcomes, decide which of the three four models is best for predicting the cost of a home. [Hint: The comparison of (d) and (b) tells you whether the quadratic terms contribute significantly, and the comparison of (d) and (c) tells you whether any of the interactive terms contribute significantly.] Part 2: Using the same data sheet, compare housing prices in (A) Manhattan, (B) Westchester, (C) Connecticut, and (D) New Jersey: (a) Is there any significant difference between housing prices in the four areas? (b) What does your regression model predict for the difference between the cost of a home in New Jersey and Westchester?
62 Topic 10 Analysis of Variance (ANOVA): Single Factor Analysis (Based on 9.1 in the book) In the language of ANOVA, we are interested in the response (dependent variable, which we called y in regression) to one or more factors (independent variables which we called x 1 , x 2 , ... in regression). These factors may be qualitative or quantitative, and their values are called levels . This is where they differ from the qualitative variables as we used them in regression. For instance, a qualitative factor may have non-numerical levels, such as Soccer, Football, etc., while quantitative ones have numerical levels. Finally, the treatments in an experiment are the levels (in a single factor experiment) or pairs of levels (in a multiple factor experiment), and the units
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- Fall '11
- Regression Analysis, R Square