Question Type 1: Calculating the Pearsons moment-correlation coefficient r for a bivariate data set Exercises

Determine the least-squares regression line $y = ax + b$ for the following dataset: $(10, 15), (20, 14), (30, 12), (40, 10)$

Calculate the Pearson product-moment correlation coefficient, $r$, for the following dataset: $(0,5), (1,6), (2,8), (3,9)$

Calculate Pearson’s product-moment correlation coefficient, $r$, for the dataset: $(10, 15), (20, 14), (30, 12), (40, 10)$

Calculate Pearson’s product-moment correlation coefficient, $r$, for the following dataset:

Compute the Pearson's product-moment correlation coefficient, $r$, for the following dataset: $(1, 2), (2, 4), (3, 6), (4, 8), (5, 10)$

Using the regression line $y = -0.17x + 17$ for the dataset $(10, 15), (20, 14), (30, 12), (40, 10)$, predict the value of $y$ when $x = 50$ and comment on the reliability of your prediction.

Find the least-squares regression line in the form $y = ax + b$ for the dataset: $(1, 2), (2, 4), (3, 6), (4, 8), (5, 10)$.

Using the regression line $y = 2x$ from the dataset $(1, 2), (2, 4), (3, 6), (4, 8), (5, 10)$, predict the value of $y$ when $x = 6$ and comment on the reliability of the prediction.

Determine the regression line $y=ax+b$ for the dataset: $(1,2), (2,3), (3,5), (4,7), (5,11)$.

Using the regression line $y = 1.4x + 4.9$ from the dataset $(0, 5), (1, 6), (2, 8), (3, 9)$, predict the value of $y$ at $x = 5$ and comment on the reliability of this prediction.

Find the regression line $y = ax + b$ for the dataset: $(0,5), (1,6), (2,8), (3,9)$.

Using the regression line $y = 2.2x - 1$ for the dataset $(1, 2), (2, 3), (3, 5), (4, 7), (5, 11)$, predict the value of $y$ at $x = 6$ and comment on the reliability of this prediction.