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

Question 1

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

[5]

Question 2

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

[3]

Question 3

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

[4]

Question 4

The question asks for the manual calculation of Pearson’s product-moment correlation coefficient for a small dataset. It tests knowledge of the relevant formula and statistical computation.

x

$x$	1	2	3	4	5
$y$	2	3	5	7	11

[3]

Question 5

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

[4]

Question 6

The question tests the application of a linear regression model to make predictions and the evaluation of the reliability of such predictions based on the range of the data used to create the model.

Using the regression line y = - 0.17 x + 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.

[4]

Question 7

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

[5]

Question 8

Using the regression line y = 2 x 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.

[4]

Question 9

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

[5]

Question 10

Using the regression line y = 1.4 x + 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.

[4]

Question 11

Finding the regression line equation for a small dataset.

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

[4]

Question 12

Using the regression line y = 2.2 x - 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.

[4]

IB Mathematics Applications & Interpretation Question Type 1: Calculating the Pearsons Moment-correlation Coefficient r for a Bivariate Data Set Exercises