The following table shows economic development measured in per capita income PCINC. Year PCINC Year PCINC 1870 340 1920 1050 1880 499 1930 1170 1890 592 1940 1364 1900 757 1950 1836 1910 927 1960 2132 Table 12.7 a. What are the independent and dependent variables? CHAPTER 12 | LINEAR REGRESSION AND CORRELATION 661 b. Draw a scatter plot. c. Use regression to find the line of best fit and the correlation coefficient. d. Interpret the significance of the correlation coefficient. e. Is there a linear relationship between the variables? f. Find the coefficient of determination and interpret it. g. What is the slope of the regression equation? What does it mean? h. Use the line of best fit to estimate PCINC for 1900, for 2000. i. Determine if there are any outliers
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 economic development measured in per capita income PCINC.
Year PCINC Year PCINC
1870 340 1920 1050
1880 499 1930 1170
1890 592 1940 1364
1900 757 1950 1836
1910 927 1960 2132
Table 12.7
a. What are the independent and dependent variables?
CHAPTER 12 | LINEAR
b. Draw a scatter plot.
c. Use regression to find the line of best fit and the correlation coefficient.
d. Interpret the significance of the correlation coefficient.
e. Is there a linear relationship between the variables?
f. Find the coefficient of determination and interpret it.
g. What is the slope of the regression equation? What does it mean?
h. Use the line of best fit to estimate PCINC for 1900, for 2000.
i. Determine if there are any outliers
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