Complete the following worksheet and then use it to calculate the coefficient of determination. ii xixi yiyi yˆy^ (yˆi−y¯)2y^i−y¯2 (yi−y¯)2yi−y¯2 1 15 160 177.649 2.719 256.000 2 13.5 220 202.382 696.010 1,936.000 3 16.5 140 152.915 532.917 1,296.000 4 14.5 190 185.893 97.871 196.000 5 17 120 144.671 981.506 3,136.000 6 16 160 161.160 220.226 256.000 7 13 210 210.627 1,199.029 1,156.000 8 18 150 128.182 2,286.561 676.000 9 12 220 227.116 2,612.845 1,936.000 10 15.5 190 169.404 43.507 196.000       Total     ?     ?   The coefficient of determination (r2r2) is:    ?   According to the regression model, which of the following is the best estimate together with the 95 percent prediction interval of paint sales (in thousands of gallons) in a sales region where the selling price is $12.50? 437.605 ± 2(17.200)   218.855 ± 2(17.200)   437.605 ± 2(3.045)   218.855 ± 2(3.045)     What is the price elasticity of demand at a selling price of $12.50? -0.58   -0.07   -0.94   -0.06

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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.