The table presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data. Four Data Sets For Exploring Correlation and Regression Data Set A  xx   1010   88   1313   99   1111   1414   66   44   1212   77   55   yy   8.048.04   6.956.95   7.587.58   8.818.81   8.338.33   9.969.96   7.247.24   4.264.26   10.8410.84   4.824.82   5.685.68  Data Set B  xx   1010   88   1313   99   1111   1414   66   44   1212   77   55   yy   9.149.14   8.148.14   8.748.74   8.778.77   9.269.26   8.108.10   6.136.13   3.103.10   9.139.13   7.267.26   4.744.74  Data Set C  xx   1010   88   1313   99   1111   1414   66   44   1212   77   55   yy   7.467.46   6.776.77   12.7412.74   7.117.11   7.817.81   8.848.84   6.086.08   5.395.39   8.158.15   6.426.42   5.735.73  Data Set D  xx   88   88   88   88   88   88   88   88   88   88   1919   yy   6.586.58   5.765.76   7.717.71   8.848.84   8.478.47   7.047.04   5.255.25   5.565.56   7.917.91   6.896.89   12.5012.50  To access the complete data sets, click the link for your preferred software format: Data Set AA Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV  CrunchIt! Data Set BB Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV  CrunchIt! Data Set CC Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV  CrunchIt! Data Set DD Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV  CrunchIt! (a) Without making scatterplots, find the correlation, to three decimal places, for all four data sets. Fill in the blanks for the value of the correlation for Set A,A, for the value of the correlation for Set B,B, for the value of the correlation for Set C,C, and for the value of the correlation for Set D,D, respectively. (Enter your answers rounded to three decimal places.) rSet A=rSet A=     rSet B=rSet B=     rSet C=rSet C=     rSet D=rSet D=     Without making scatterplots, find the least‑squares regression line for all four data sets. What do you notice about the least-squares regression lines? Choose the correct answer. The least‑squares regression lines are approximately the same for all four data sets. The least‑squares regression lines for Data Sets BB and CC are the same, but different from Data Sets AA and D.D. The least‑squares regression line for each data set is markedly different. The least‑squares regression lines for Data Sets AA and CC are the same, but different from Data Sets BB and D.D. Use the regression line to predict ^yy^ for x=10.x=10. (Enter your answer rounded to a whole number.) ^y=y^=     (b) Make a scatterplot for each of the data sets, and add the regression line to each plot. Select the correct set of a scatterplots with regression lines for Set A,A, Set B,B, Set C,C, and Set D,D, respectively.         (c) In which of the four cases would you be willing to use the regression line to describe the dependence of yy on x?x? Set BB Set CC Set AA Set DD

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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.