Explanation Given info: The data related to produced chips and cost per chips for each year. Calculation: Scatterplot : Software procedure: Step by step procedure to draw scatterplot using MINITAB software is given as, Choose Graph > Scatterplot . Choose Simple , and then click OK . In Y-variables , enter the column of Cost per chips . In X-variables enter the column of Chips . Click OK . The output using MINITAB software is given as, There is a strong, curved and negative association between cost per chips and produced chips strong, curved and negative. It can be said that the cost per chip is getting less for larger number of produced chips. The linear model is not appropriate for this type of curved data. Re-expression of data is needed. One can use logarithm of cost per chip as a response variable and logarithm of number of produced chips to straighten the data. Transformation of response variable : Choose Calc > Calculator . Choose Log(Cost per chip) in the Store result in variable box. In Expression box, type LOGTEN(‘Cost per chip’). Click OK . The transformed response variable is stored in the column named Log(Cost per chip) , which is given below: Cost per chip Log(Cost per chip) 146.1 2.16465 105.8 2.024486 85.75 1.933234 77.02 1.886604 66.1 1.820201 63.92 1.805637 58.8 1.769377 50.91 1.706803 47.22 1.674126 44.31 1.646502 42.88 1.632255 39.05 1.591621 37.47 1.573684 35.09 1.545183 34.04 1.53199 Now, one can use Log(Cost per chip) as response variable. Transformation of predictor variable : Choose Calc > Calculator . Choose Log(Chips) in the Store result in variable box. In Expression box, type LOGTEN(‘Chips’). Click OK . The transformed predictor variable is stored in the column named Log(Chips), which is given below: Chips Log(Chips) 10 1 20 1.30103 30 1.477121 40 1.60206 50 1.69897 60 1.778151 70 1.845098 80 1.90309 90 1.954243 100 2 120 2.079181 140 2.146128 160 2.20412 180 2.255273 200 2.30103 Now, one can use Log(Chips) as predictor variable. Linear regression model: A linear regression model is given as y ^ = b 0 + b 1 x where be the predicted values of response variable and x be the predictor variable. The b 1 be the slope and b 0 be the intercept of the line. Regression Software procedure: Step by step procedure to get the output using MINITAB software is given as, Choose Stat > Regression > Regression > Fit Regression Model

4th Edition

ISBN: 9780321826275

Author: Richard D. De Veaux

Publisher: PEARSON

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