2. Now Kelly considers the number of replaced parts in her study. a) She creates

Question

2. Now Kelly considers the number of replaced parts in her study. a) She creates a scatterplot (Item F of selling price versus number of replaced parts According to the plot, describe what appears to be the relationship between the number of replaced parts and the selling price. Be brief and as specific as possible. b) She fits a surface to the data, as summarized in ltem G. What is the predicted selling price equation for the surface fit? Since there are now two explanatory variables, clearly define what each represents in words. c) Interpret the value of the intercept estimate, bo, for this predicted selling price equation. Use the story' context. s d) Explain what is suggested by the value of R2 for the surface fit, in relation to y and y. e) The formula for R2 has the form [(a c)2 (a c) b1)2 (a2 -b2)2 a1 (a c)2 (az c)2 where the subscript i for the a's and b's refers to the i-th sale (or, the i-th row of the data). For the fitted surface, identify or calculate a a2, br, b2, and c. Using the notation in part (e) above, what are the values for ai b called? g she creates a residual plot (Item H) of residuals against the predicted selling price for the surface fit. She finds the plot satisfactory (at least an improvement from the previous residual plot). However, she notes that predictions of selling prices beyond 7000 could be problematic. In one sentence, describe what she sees in the plot that led to her concern.

Explanation / Answer

a) Based on the ITEM F , it is evident that there is a linear relationship between between price sold and the # of replaced parts but in the negative direction, That is as the # of replaced parts increases thr price value decreases and vice versa

b) Lets look at the paramter estaimates table and for the equation using the cofficeients as

Price = 9258.647 -0.489*SatisfactionIndex -251.2# Number of replaced parts +2.15*#of repalced parts*#of replaced parts

c) The intercept value is 9258.647 , which means that if all independent variables are considered 0 , then the price would be 9258.647 , it is the point where X=0 and the line cuts the Y axis .

d) R2 is a metric that explains the variatin captured by the model. It ranges from 0 to 1 , higher the value better the model. As the r2 value i s 0.8376 , this means that the model is able to capture 83.76% of the variation of the data

Hope this helps !!

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