An employee starts working in Year 1 with a salary of $50,000. Each year her salary...

 

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An employee starts working in Year 1 with a salary of $50,000. Each year her salary increases by approximately 5%. By Year 20 she is earning $126,000. Aspects of a basic analysis are shown in the figure. (spueseous) K Log salary 120 COL OR 09 4.8 46 44 4.2 40 oooooooooooooo (8) ooooo 5 10 Years of Employment (C) 15 10 15 0000000 00000000 Years of Employment 20 B Koso promo 9 4 D Z 9000 -0.006 -0.015 T 0 0 0 0 O O 00 5 C 000 (D) O O 10 Years of Employment 00 (d) 00 0 10 15 O 15 Years of Employment O B 8 20 Panel (a) shows a scatterplot of salary against year, with the least squares regression line. The value of r2 for these data is 0.9832. Panel (b) is a plot of the residuals against year. Panel (e) is a scat- terplot with the least -squares regression line for log salary against year. For this model, r2 = 0.9995. Panel (d) is a plot of the residuals for the model using year to predict log salary. (a) Describe the relationship between salary and year. (b) What percent of the variation in salary is explained by Year? Would you say that this is an indication of a strong linear rela- tionbship? Explain your answer. (e) Interpret the residual plot in panel (b). (d) Explain how the residual plot (panel (b)) highlights the devia - tions from the least -squares regression line (panel (a)). (e) Compare panel (c) with panel (a). What are the similarities and differences ? (f) Compare panel (d) with panel (b). What are your findings? An employee starts working in Year 1 with a salary of $50,000. Each year her salary increases by approximately 5%. By Year 20 she is earning $126,000. Aspects of a basic analysis are shown in the figure. (spueseous) K Log salary 120 COL OR 09 4.8 46 44 4.2 40 oooooooooooooo (8) ooooo 5 10 Years of Employment (C) 15 10 15 0000000 00000000 Years of Employment 20 B Koso promo 9 4 D Z 9000 -0.006 -0.015 T 0 0 0 0 O O 00 5 C 000 (D) O O 10 Years of Employment 00 (d) 00 0 10 15 O 15 Years of Employment O B 8 20 Panel (a) shows a scatterplot of salary against year, with the least squares regression line. The value of r2 for these data is 0.9832. Panel (b) is a plot of the residuals against year. Panel (e) is a scat- terplot with the least -squares regression line for log salary against year. For this model, r2 = 0.9995. Panel (d) is a plot of the residuals for the model using year to predict log salary. (a) Describe the relationship between salary and year. (b) What percent of the variation in salary is explained by Year? Would you say that this is an indication of a strong linear rela- tionbship? Explain your answer. (e) Interpret the residual plot in panel (b). (d) Explain how the residual plot (panel (b)) highlights the devia - tions from the least -squares regression line (panel (a)). (e) Compare panel (c) with panel (a). What are the similarities and differences ? (f) Compare panel (d) with panel (b). What are your findings?