The following are the weight (in grams) and quantity of volatile emissions (in hundreds of nanograms) for plants. A scatterplot of the data is giveh to the right. Ay 30 20 Weight (x) 57 86 59 66 51 66 63 81 78 54 9 10主 Quantity (y) 0 40 60 80 100 8.0 22.0 11.0 22.0 12.5 11.0 8.0 13.5 17.5 21.0 a. Obtain the linear correlation coefficient. b. Interpret the value of r in terms of the linear relationship between the two variables. c. Discuss the graphical interpretation of the value of r. d. Obtain the value of the coefficient of determination by squaring r. a. r= (Round to three decimal places as needed.)
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Correlation Coefficient:
It is one of the statistical measures. It is used between any two variables in order to know the strength of the linear relationship of those two variables. The value of the correlation coefficient lies between -1 to 1(including zero).
If the correlation coefficient positive then it is positively linearly correlated, if it is negative then it is negatively linearly correlated, and if it is zero then there is no linear correlation between the variables. When the correlation coefficient reaching the maximum or the minimum value (i.e., -1 or1) then the variables are very strongly related to each other.
r=, Cov(x,y) is the covariance of x and y; is the standard deviation of x; is the standard deviation of y.
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