Question

PM ENG 6/5/2019 Personal Income- Saginaw Interpreting Rates of Change 99 When am I ever qoing to use this? e able to determine the concepts in this worksheet, the meanina of rates of change in real world contexts The U.S. Bureau of living in various areas throurh s and reports the combined personal incomes of people income of all people living in a designated geographical area, the bureau also renorts pernal reports income per capita. (Per capita means per person.) The table below shows the personal income and the personal income per capita for people living in naw owWnship North metropolitan area of Michigan (Source: Statistical Abstract of the Table 661). t Personal Income Personal Income Per Capita (million dollars) (thousand dollars) 1980 2259 9.9 1990 1995 2000 3492 16.5 4373 20.6 5374 25.6 2001 5356 25.6 2002 5289 25.2 2003 5460 26.1 2004 5580 26.7 2005 5665 27.3 1. Calculate the average rate of change in personal income and in personal income per capita between 1980 and 2005. average role of change in pusunal Incone: in prsanal incame per Eapita: Math 107 Workbook 2. Linear functions have constant rates of change. Calculate the ratee results of Exercise 1 personal income per capita between200 personal income mal income and , determine if are linear functions of time. personal income per capit 3. Draw a scatter plot of Personal Income Per Capita as a function of Personal Income. Then sketch a line to model the data. 4. The equation of the line of best fit for the data is y 0.00502x-1.33. What is the meaning of the slope of the line in this context? 58 Math 107 Workbook

Answer 1

1)

1980-2005 SUMMARY OUTPUT Regression Statistics Multiple R 0.998780811 R Square Adjusted R Square 0.997563107 0.99721498 Standard Error 61.89922351 Observations 9 ANOVA gnificance F SS MS Regression 1 10979244.29 10979244.29 2865.510777 2.08E-10 Residual 26820.5971 7 3831.513871 Total 11006064.89 Standard Error P-value Lower 95% Lower 95.0% Upper 95.0% Coefficients t Stat Upper 95% 223.0276708 0.037755134 16.72262 Intercept 87.24644131 2.556295333 429.3327217 16.72261981 429.332722 Personal Income per capita 201.6827208 3.767624987 210.5917382 53.53046588 2.081E-10 192.7737 192.7737034 210.591738

Average rate of change would be 223.028

2)

Here rate of change means change in y due to x.

2000-200 SUMMARY OUTPUT Regression Statistics Multiple R 0 0 Square Adjusted R Square -1 Standard Error 12.72792206 Observations 2 ANOVA df SS MS Significance F 1 #NUM! Regression 0 0 0 Residual 162 162 1 Total 162 2 Coefficients Standard Error P-value Lower 95% Lower 95,0% Upper 95.0% t Stat Upper 95% 5479.355843 596.1111111 5250.644157 Intercept 5365 0.001067954 5250.644157 5479.355843 Variable 1 #NUM! 0 65535 0 C 0 C

For, 2000-2001, rate of change would be 0.

3) Scatter plot would be as followed:

Personal Income per capita Personal Income 1980 9.9 2259 1980 1990 3492 16.5 1990 1995 20.6 4373 1995 2000 25.6 5374 2000 2001 25.6 5356 2001 25. 2002 7000 26 2003 6000 2004 26. y 142.3x-27953 2005 26. 5000 Personal Income per capita 4000 Personal Income 3000 Linear (Personal Income) 2000 1000 0 1970 1980 1990 2000 2010

4)

y=0,00502x-1.33

In this context, y is a dependent variable slope is 0.00502 and x is independent variable, here the slope shows that the 0.00502 amount change in x would be the rate change in the y.

In simple words slope states the rate of change in y due to changes in x.