In: Math
The paired data ((x, y)): (1,6),(5,8),(7,9),(8,0),(4,1) is considered.
(a) Find the pearson correlation coefficient
(b) Find the slope and intercept of the regression coeffients.
(c) What percent of the variation in y is described by variation in x?
Some statistics are not resistant to a single outlier. An example would be the mean value, as one extremely large of small value can tip the scales. Which of these statistics is also not resistant to outliers: median, standard deviation, IQR, range, Pearson correlation, linear regression coefficients?
(a) Find the pearson correlation coefficient
correlation coefficient r = -0.16
(b) Find the slope and intercept of the regression coeffients.
y = -0.2333x + 5.9667
slope = -0.2333
Intercept = 5.9667
(c) What percent of the variation in y is described by variation in x?
The coefficient of determination, r2, is a measure of how well the variation of one variable explains the variation of the other, and corresponds to the percentage of the variation explained by a best-fit regression line which is calculated for the data
R2 = 0.0245
so 2.45% of the variation y is described by variation in x?
Which of these statistics is also not resistant to outliers:
Outliers are calculate based on the IQR
IQR is measured from quartile 3 and quartile 3.
Quartile 3 - Quartile 1 = IQR
Apart from IQR all other statistics mentioned are not resistant to outliers