Question

Temperature, x 72 85 91 90 88 98 75 100 80

Number of absences, y 3 7 10 10 8 15 4 15 5
Computer the linear correlation coefficient between temperature and number of absences

Answer 1

The equation of the regression line is
`\bar y` = 0.449x + 30.27. Option A is the right choice.

The mean of x (temperature) and y (number of absences).

Mean of x = (72 + 85 + 91 + 90 + 88 + 98 + 75 + 100 + 80) / 9 = 87.22

Mean of y = (3 + 7 + 10 + 10 + 8 + 15 + 4 + 15 + 5) / 9 = 8.89

The deviations from the mean for each data point.

Deviation of x for temperature 72 = 72 - 87.22 = -15.22

Deviation of y for absences 3 = 3 - 8.89 = -5.89

Do this for all data points.

The product of the deviations from the mean for each data point.

Product of deviations for temperature 72 and absences 3 = -15.22 * -5.89 = 88.98

Do this for all data points.

The variance of x.

Variance of x = sum of squares of deviations from the mean of x / (number of data points - 1)

Variance of x = (-15.22)^2 + ... + (12.78)^2 / (9 - 1)

Variance of x = 195.44

The slope (m) of the regression line.

m = sum of products of deviations from the mean / variance of x

m = (-15.22 * -5.89 + ... + 12.78 * 0.11) / 195.44

m = 0.449

The y-intercept (b) of the regression line.

b = mean of y - (m * mean of x)

b = 8.89 - (0.449 * 87.22)

b = 30.27

The equation of the regression line is:
`\bar y` = mx + b

Therefore, the equation of the regression line for this data is:

`\bar y` = 0.449x + 30.27

Option A is the right choice.

For complete question refer to image: