Using SPSS, estimate a simple linear regression model and find the value of the parameters for the estimation of new motor vehicle sales from real disposable income per person. b) Interpret the intercept and the slope coefficients. c) State the correlation coefficient and the coefficient of determination. Interpret the coefficient of determination.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The following table shows data on new motor vehicle sales and the real personal disposable income per person in Canada between 1981 and 2001.
|
Year |
New motor vehicles sales (units) |
Real personal disposable income per person (1992 $) |
|
1981 |
1190882 |
16368 |
|
1982 |
920902 |
16107 |
|
1983 |
1081088 |
15765 |
|
1984 |
1283502 |
16252 |
|
1985 |
1530410 |
16710 |
|
1986 |
1515920 |
16747 |
|
1987 |
1533637 |
16856 |
|
1988 |
1565501 |
17443 |
|
1989 |
1483875 |
17875 |
|
1990 |
1317869 |
17756 |
|
1991 |
1287790 |
17165 |
|
1992 |
1227419 |
17096 |
|
1993 |
1192934 |
17016 |
|
1994 |
1260056 |
17000 |
|
1995 |
1166535 |
17047 |
|
1996 |
1204557 |
16861 |
|
1997 |
1424380 |
16994 |
|
1998 |
1428932 |
17334 |
|
1999 |
1542041 |
17735 |
|
2000 |
1587561 |
18068 |
|
2001 |
1597949 |
18185 |
a) Using SPSS, estimate a simple linear regression model and find the value of the parameters for the estimation of new motor vehicle sales from real disposable income per person.
b) Interpret the intercept and the slope coefficients.
c) State the
d) Confirm the intercept, slope and correlation coefficient by computing them without SPSS.
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