Question

1. (20 pts) Use the “Distance.sav” (SPSS) data set (located below) to perform a linear regression analysis. This dataset shows how far on average a person in Illinois drives each year. Write your findings using the format presented in the class slides. (2 pts) How much of the variation in the dependent variable is explained by the variation in the independent variable? What statistic did you use? (2 pts) Is the linear model significantly different than zero? Why or why not? What statistic did you use? (4 pts) Do the model assumptions hold? Why or why not? Provide a thorough response. (Hint: Create both a Histogram and a Normal probability plot using the standardized residuals. Also create a scatterplot of Regression Standardized Residuals and the Regression Standardized Predicted Value of the dependent variable. Attach a copy of each below.)

Year	Distance
1960	1472.08
1961	1564.80
1962	1603.03
1963	1670.65
1964	1840.97
1965	1936.46
1966	2031.93
1967	2093.46
1968	2163.59
1969	2205.16
1970	2281.37
1971	2398.31
1972	2503.06
1973	2623.12
1974	2575.82
1975	2604.13
1976	2740.65
1977	2791.32
1978	2886.16
1979	2870.89
1980	3049.89
1981	3107.49
1982	3202.19
1983	3240.61
1984	3400.64
1985	3461.57
1986	3617.96
1987	3887.96
1988	4148.67
1989	4476.36
1990	4506.32
1991	4499.51
1992	4487.92
1993	4470.72
1994	4559.77
1995	4636.48
1996	4745.51
1997	4831.20
1998	4897.49
1999	4978.39
2000	4958.52
2001	5024.30
2002	5131.16
2003	5152.03

Answer 1

98.3% of total variation in the dependent variable is explained by the variation in the independent variable. Here we use R² statistic.

From t test corresponding Year, we see that p-value=0.000<0.05, so the linear model is significantly different than zero. Here we use t statistic and observed value of this statistic=49.15.

From normal probability plot, we see that assumption of normality holds. Since the points are randomly distributed on both sides of horizontal line in residual plot, assumption of linearity and equal variance hold. However from fitted vs. standard residual plot, one value of standardized residual greater than 3, so outlier may present.