Economist A.W. Phillips was one of the first economists to present compelling evidence of the correlation between unemployment and wage inflation. Since wages and salaries are a major input cost for companies, rising wages should lead to higher prices for products and services in an economy, ultimately pushing the overall inflation rate higher. As a result, Phillips graphed the relationship between general price inflation and unemployment, rather than wage inflation. Data on unemployment (independent) and inflation (dependent) from the Federal Reserve is on the Excel workbook. Find the equation for the regression line for this data. Find the correlation coefficient and R2. Using the data, is the correlation statistically significant at the 1% level? Federal Reserve Economic Data https://fred.stlouisfed.org/graph/?g=3obN Observation date Unemployment Rate Inflation Rate 1 1960-01-01 5.2 1.2 2 1961-01-01 6.6 1.6 3 1962-01-01 5.8 0.7 4 1963-01-01 5.7 1.3 5 1964-01-01 5.6 1.6 6 1965-01-01 4.9 1.1 7 1966-01-01 4.0 1.9 8 1967-01-01 3.9 3.2 9 1968-01-01 3.7 3.6 10 1969-01-01 3.4 4.7 11 1970-01-01 3.9 6.2 12 1971-01-01 5.9 5.3 13 1972-01-01 5.8 3.3 14 1973-01-01 4.9 3.6 15 1974-01-01 5.1 9.6 16 1975-01-01 8.1 11.8 17 1976-01-01 7.9 6.7 18 1977-01-01 7.5 5.2 19 1978-01-01 6.4 6.8 20 1979-01-01 5.9 9.3 21 1980-01-01 6.3 13.9 22 1981-01-01 7.5 11.8 23 1982-01-01 8.6 8.3 24 1983-01-01 10.4 3.7 25 1984-01-01 8.0 4.3 26 1985-01-01 7.3 3.5 27 1986-01-01 6.7 4.0 28 1987-01-01 6.6 1.4 29 1988-01-01 5.7 4.1 30 1989-01-01 5.4 4.5 31 1990-01-01 5.4 5.2 32 1991-01-01 6.4 5.6 33 1992-01-01 7.3 2.7 34 1993-01-01 7.3 3.3 35 1994-01-01 6.6 2.5 36 1995-01-01 5.6 2.9 37 1996-01-01 5.6 2.8 38 1997-01-01 5.3 3.0 39 1998-01-01 4.6 1.6 40 1999-01-01 4.3 1.7 41 2000-01-01 4.0 2.8 42 2001-01-01 4.2 3.7 43 2002-01-01 5.7 1.2 44 2003-01-01 5.8 2.8 45 2004-01-01 5.7 2.0 46 2005-01-01 5.3 2.8 47 2006-01-01 4.7 4.0 48 2007-01-01 4.6 2.1 49 2008-01-01 5.0 4.3 50 2009-01-01 7.8 -0.1 51 2010-01-01 9.8 2.6 52 2011-01-01 9.1 1.7 53 2012-01-01 8.3 3.0 54 2013-01-01 8.0 1.7 55 2014-01-01 6.6 1.6 56 2015-01-01 5.7 -0.2 57 2016-01-01 4.8 1.2 58 2017-01-01 4.7 2.5 59 2018-01-01 4.0 2.1 60 2019-01-01 4.0 1.5 61 2020-01-01 3.5 2.5 62 2021-01-01 6.3 1.4
Economist A.W. Phillips was one of the first economists to present compelling evidence of the correlation between unemployment and wage inflation. Since wages and salaries are a major input cost for companies, rising wages should lead to higher prices for products and services in an economy, ultimately pushing the overall inflation rate higher. As a result, Phillips graphed the relationship between general price inflation and unemployment, rather than wage inflation. Data on unemployment (independent) and inflation (dependent) from the Federal Reserve is on the Excel workbook. Find the equation for the regression line for this data. Find the correlation coefficient and R2. Using the data, is the correlation statistically significant at the 1% level? Federal Reserve Economic Data https://fred.stlouisfed.org/graph/?g=3obN Observation date Unemployment Rate Inflation Rate 1 1960-01-01 5.2 1.2 2 1961-01-01 6.6 1.6 3 1962-01-01 5.8 0.7 4 1963-01-01 5.7 1.3 5 1964-01-01 5.6 1.6 6 1965-01-01 4.9 1.1 7 1966-01-01 4.0 1.9 8 1967-01-01 3.9 3.2 9 1968-01-01 3.7 3.6 10 1969-01-01 3.4 4.7 11 1970-01-01 3.9 6.2 12 1971-01-01 5.9 5.3 13 1972-01-01 5.8 3.3 14 1973-01-01 4.9 3.6 15 1974-01-01 5.1 9.6 16 1975-01-01 8.1 11.8 17 1976-01-01 7.9 6.7 18 1977-01-01 7.5 5.2 19 1978-01-01 6.4 6.8 20 1979-01-01 5.9 9.3 21 1980-01-01 6.3 13.9 22 1981-01-01 7.5 11.8 23 1982-01-01 8.6 8.3 24 1983-01-01 10.4 3.7 25 1984-01-01 8.0 4.3 26 1985-01-01 7.3 3.5 27 1986-01-01 6.7 4.0 28 1987-01-01 6.6 1.4 29 1988-01-01 5.7 4.1 30 1989-01-01 5.4 4.5 31 1990-01-01 5.4 5.2 32 1991-01-01 6.4 5.6 33 1992-01-01 7.3 2.7 34 1993-01-01 7.3 3.3 35 1994-01-01 6.6 2.5 36 1995-01-01 5.6 2.9 37 1996-01-01 5.6 2.8 38 1997-01-01 5.3 3.0 39 1998-01-01 4.6 1.6 40 1999-01-01 4.3 1.7 41 2000-01-01 4.0 2.8 42 2001-01-01 4.2 3.7 43 2002-01-01 5.7 1.2 44 2003-01-01 5.8 2.8 45 2004-01-01 5.7 2.0 46 2005-01-01 5.3 2.8 47 2006-01-01 4.7 4.0 48 2007-01-01 4.6 2.1 49 2008-01-01 5.0 4.3 50 2009-01-01 7.8 -0.1 51 2010-01-01 9.8 2.6 52 2011-01-01 9.1 1.7 53 2012-01-01 8.3 3.0 54 2013-01-01 8.0 1.7 55 2014-01-01 6.6 1.6 56 2015-01-01 5.7 -0.2 57 2016-01-01 4.8 1.2 58 2017-01-01 4.7 2.5 59 2018-01-01 4.0 2.1 60 2019-01-01 4.0 1.5 61 2020-01-01 3.5 2.5 62 2021-01-01 6.3 1.4
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
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Question
- Economist A.W. Phillips was one of the first economists to present compelling evidence of the
correlation between unemployment and wage inflation. Since wages and salaries are a major input cost for companies, rising wages should lead to higher prices for products and services in an economy, ultimately pushing the overall inflation rate higher. As a result, Phillips graphed the relationship between general price inflation and unemployment, rather than wage inflation. Data on unemployment (independent) and inflation (dependent) from the Federal Reserve is on the Excel workbook.- Find the equation for the regression line for this data.
- Find the
correlation coefficient and R2. - Using the data, is the correlation statistically significant at the 1% level?
| Federal Reserve Economic Data | |||
| https://fred.stlouisfed.org/graph/?g=3obN | |||
| Observation date | Unemployment Rate | Inflation Rate | |
| 1 | 1960-01-01 | 5.2 | 1.2 |
| 2 | 1961-01-01 | 6.6 | 1.6 |
| 3 | 1962-01-01 | 5.8 | 0.7 |
| 4 | 1963-01-01 | 5.7 | 1.3 |
| 5 | 1964-01-01 | 5.6 | 1.6 |
| 6 | 1965-01-01 | 4.9 | 1.1 |
| 7 | 1966-01-01 | 4.0 | 1.9 |
| 8 | 1967-01-01 | 3.9 | 3.2 |
| 9 | 1968-01-01 | 3.7 | 3.6 |
| 10 | 1969-01-01 | 3.4 | 4.7 |
| 11 | 1970-01-01 | 3.9 | 6.2 |
| 12 | 1971-01-01 | 5.9 | 5.3 |
| 13 | 1972-01-01 | 5.8 | 3.3 |
| 14 | 1973-01-01 | 4.9 | 3.6 |
| 15 | 1974-01-01 | 5.1 | 9.6 |
| 16 | 1975-01-01 | 8.1 | 11.8 |
| 17 | 1976-01-01 | 7.9 | 6.7 |
| 18 | 1977-01-01 | 7.5 | 5.2 |
| 19 | 1978-01-01 | 6.4 | 6.8 |
| 20 | 1979-01-01 | 5.9 | 9.3 |
| 21 | 1980-01-01 | 6.3 | 13.9 |
| 22 | 1981-01-01 | 7.5 | 11.8 |
| 23 | 1982-01-01 | 8.6 | 8.3 |
| 24 | 1983-01-01 | 10.4 | 3.7 |
| 25 | 1984-01-01 | 8.0 | 4.3 |
| 26 | 1985-01-01 | 7.3 | 3.5 |
| 27 | 1986-01-01 | 6.7 | 4.0 |
| 28 | 1987-01-01 | 6.6 | 1.4 |
| 29 | 1988-01-01 | 5.7 | 4.1 |
| 30 | 1989-01-01 | 5.4 | 4.5 |
| 31 | 1990-01-01 | 5.4 | 5.2 |
| 32 | 1991-01-01 | 6.4 | 5.6 |
| 33 | 1992-01-01 | 7.3 | 2.7 |
| 34 | 1993-01-01 | 7.3 | 3.3 |
| 35 | 1994-01-01 | 6.6 | 2.5 |
| 36 | 1995-01-01 | 5.6 | 2.9 |
| 37 | 1996-01-01 | 5.6 | 2.8 |
| 38 | 1997-01-01 | 5.3 | 3.0 |
| 39 | 1998-01-01 | 4.6 | 1.6 |
| 40 | 1999-01-01 | 4.3 | 1.7 |
| 41 | 2000-01-01 | 4.0 | 2.8 |
| 42 | 2001-01-01 | 4.2 | 3.7 |
| 43 | 2002-01-01 | 5.7 | 1.2 |
| 44 | 2003-01-01 | 5.8 | 2.8 |
| 45 | 2004-01-01 | 5.7 | 2.0 |
| 46 | 2005-01-01 | 5.3 | 2.8 |
| 47 | 2006-01-01 | 4.7 | 4.0 |
| 48 | 2007-01-01 | 4.6 | 2.1 |
| 49 | 2008-01-01 | 5.0 | 4.3 |
| 50 | 2009-01-01 | 7.8 | -0.1 |
| 51 | 2010-01-01 | 9.8 | 2.6 |
| 52 | 2011-01-01 | 9.1 | 1.7 |
| 53 | 2012-01-01 | 8.3 | 3.0 |
| 54 | 2013-01-01 | 8.0 | 1.7 |
| 55 | 2014-01-01 | 6.6 | 1.6 |
| 56 | 2015-01-01 | 5.7 | -0.2 |
| 57 | 2016-01-01 | 4.8 | 1.2 |
| 58 | 2017-01-01 | 4.7 | 2.5 |
| 59 | 2018-01-01 | 4.0 | 2.1 |
| 60 | 2019-01-01 | 4.0 | 1.5 |
| 61 | 2020-01-01 | 3.5 | 2.5 |
| 62 | 2021-01-01 | 6.3 | 1.4 |
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