Linear Regression

1. Calculate the mean yearly value using the average gas prices by month found in the next table:
Series Id: APU000074714
Area: U.S. city average
Item: Gasoline, unleaded regular, per gallon/3.785 liters
Years: 1982 to 2011
 

Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean
1982 1.358 1.334 1.284 1.225 1. 237 1.309 1.331 1.323 1.307 1.295 1.283 1.260 1.296
1983 1.230 1.187 1.152 1.215 1.259 1.277 1.288 1.285 1.274 1.255 1.241 1.231 1.241
1984 1.216 1.209 1.210 1.227 1.236 1.229 1.212 1.196 1.203 1.209 1.207 1.193 1.212
1985 1.148 1.131 1.159 1.205 1.231 1.241 1.242 1.229 1.216 1.204 1.207 1.208 1.202
1986 1.194 1.120 0.981 0.888 0.923 0.955 0.890 0.843 0.860 0.831 0.821 0.823 0.927
1987 0.862 0.905 0.912 0.934 0.941 0.958 0.971 0.995 0.990 0.976 0.976 0.961 0.948
1988 0.933 0.913 0.904 0.930 0.955 0.955 0.967 0.987 0.974 0.957 0.949 0.930 0.946
1989 0.918 0.926 0.940 1.065 1.119 1.114 1.092 1.057 1.029 1.027 0.999 0.980 1.022
1990 1.042 1.037 1.023 1.044 1.061 1.088 1.084 1.190 1.294 1.378 1.377 1.354 1.164
1991 1.247 1.143 1.082 1.104 1.156 1.160 1.127 1.140 1.143 1.122 1.134 1.123 1.140
1992 1.073 1.054 1.058 1.079 1.136 1.179 1.174 1.158 1.158 1.154 1.159 1.136 1.127
1993 1.117 1.108 1.098 1.112 1.129 1.130 1.109 1.097 1.085 1.127 1.113 1.070 1.108
1994 1.043 1.051 1.045 1.064 1.080 1.106 1.136 1.182 1.177 1.152 1.163 1.143 1.112
1995 1.129 1.120 1.115 1.140 1.200 1.226 1.195 1.164 1.148 1.127 1.101 1.101 1.147
1996 1.129 1.124 1.162 1.251 1.323 1.299 1.272 1.240 1.234 1.227 1.250 1.260 1.231
1997 1.261 1.255 1.235 1.231 1.226 1.229 1.205 1.253 1.277 1.242 1.213 1.177 1.234
1998 1.131 1.082 1.041 1.052 1.092 1.094 1.079 1.052 1.033 1.042 1.028 0.986 1.059
1999 0.972 0.955 0.991 1.177 1.178 1.148 1.189 1.255 1.280 1.274 1.264 1.298 1.165
2000 1.301 1.369 1.541 1.506 1.498 1.617 1.593 1.510 1.582 1.559 1.555 1.489 1.510
2001 1.472 1.484 1.447 1.564 1.729 1.640 1.482 1.427 1.531 1.362 1.263 1.131 1.461
2002 1.139 1.130 1.241 1.407 1.421 1.404 1.412 1.423 1.422 1.449 1.448 1.394 1.358
2003 1.473 1.641 1.748 1.659 1.542 1.514 1.524 1.628 1.728 1.603 1.535 1.494 1.591
2004 1.592 1.672 1.766 1.833 2.009 2.041 1.939 1.898 1.891 2.029 2.010 1.882 1.880
2005 1.823 1.918 2.065 2.283 2.216 2.176 2.316 2.506 2.927 2.785 2.343 2.186 2.295
2006 2.315 2.310 2.401 2.757 2.947 2.917 2.999 2.985 2.589 2.272 2.241 2.334 2.589
2007 2.274 2.285 2.592 2.860 3.130 3.052 2.961 2.782 2.789 2.793 3.069 3.020 2.801
2008 3.047 3.033 3.258 3.441 3.764 4.065 4.090 3.786 3.698 3.173 2.151 1.689 3.266
2009 1.787 1.928 1.949 2.056 2.265 2.631 2.543 2.627 2.574 2.561 2.660 2.621 2.350
2010 2.731 2.659 2.780 2.858 2.869 2.736 2.736 2.745 2.704 2.795 2.852 2.985 2.788
2011 3.091 3.167 0.522

2. Using the years as your x-axis and the annual mean as your y-axis, create
o a scatter plot and
o a linear regression line.

 3. Answer the following questions using your scatter plot and linear regression line:
o What is the slope of the linear regression line?
o What is the Y-intercept of the linear regression line?
o What is the equation of the linear regression line in slope-intercept form?
o Based on the linear regression line, what would be an estimated cost of gas in the year 2020?
o What are the residuals of each year?
o Select a current price that you have seen or paid recently for gas. Is that price within the range of the linear regression line or is it an outlier? Is it within the confidence interval of 5% or either end?