Find the prediction model and predict the total price index (total) when the price index durable goods (durable) is 98.3.

(20 pts) Statistics Canada produces consumer price indexes for several different categories. The twenty years of data (Table 2) below shows the indexes for durable goods (durable), semi-durable goods (semi), non-durable goods (non), and a total price index (total) with 2002 as the base year. The year is included as a predictor variable, as an attempt to involve inflation. Please note the descriptive statistics (Table 3) listed after the data. Table 2 year durable semi non total 1986 79.5 71.5 65.5 69.8 1987 82 74.5 68.4 72.6 1988 85.1 78.2 70.5 75.2 1989 88.9 81.7 73.9 78.4 1990 89.5 84 78.5 81.6 1991 89.4 91.9 83.2 85.7 1992 90.4 92.5 83.8 86.4 1993 92.5 93.4 85.2 87.8 1994 96 94.2 81.6 86.8 1995 99 94.9 82.9 88.4 1996 100.8 95.4 84.4 89.9 1997 101.6 97 86 91.2 1998 101.5 97.7 86.1 91.4 1999 101.5 99.2 88.4 93.1 2000 100.8 99.6 93.3 96 2001 100.1 100.3 97.4 98.4 2002 100 100 100 100 2003 99.2 98.6 104.3 101.9 2004 97.5 98.2 107.9 103.4 2005 96.9 97.7 112.6 105.8 Table 3: Descriptive Statistics: durable, semi, non, total Variable N Mean StDev Variance durable 20 94.61 6.96 48.49 semi 20 92.03 8.97 80.45 non 20 86.70 12.80 163.96 total 20 89.19 10.16 103.23 (a) Regress the variable total on the variable durable. Find simple linear regression model, and in- terpret the slope in words. Er = 179942.34, >_ If = 1892.2, > my: = 169876.05, >_, y: = 1783.8, ? = 161058.44