Question

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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 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?

Expert Solution

(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

milcah answered 3 months ago

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