Please answer the following problem. Its finding equation out from the table. Th
ID: 3333885 • Letter: P
Question
Please answer the following problem. Its finding equation out from the table.
The numbers of executions carried out in a country for the years 1984 through 2005 are given in the table Year 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 Executions 21 14 14 9 18 20 23 29 Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Executions 62 63 67 75 80 76 78 73 62 52 39 49 (a) Find the cubic function that best fits the data, using x as the number of years past 1979. (Round your coefficients to three decimal places.)Explanation / Answer
The statistical software output for this problem is:
Polynomial Regression Results:
Dependent Variable: y
Independent Variable: x
y = 102.46198 + -27.073567 X + 2.4353086 X^2 + -0.057256778 X^3
Parameter estimates
Analysis of variance table for polynomial regression model:
Summary of fit:
Root MSE: 2.2886562
R-squared: 0.9924
R-squared (adjusted): 0.9912
Hence,
y = 102.462 - 27.074 x + 2.435 x2 - 0.057 x3
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 102.46198 7.0782554 0 18 14.475598 <0.0001 X -27.073567 1.6520947 0 18 -16.387418 <0.0001 X^2 2.4353086 0.11521402 0 18 21.137259 <0.0001 X^3 -0.057256778 0.0024604087 0 18 -23.271247 <0.0001