Question

linear regression
below is data on how many absences a student has each semester in a statistics class and their overall
average for the class:

absences for semester (x):	0	2	5	6

a.) would you say the data has a positive correlation or negative correlation?

• negative
• positive

b.) compute $\sigma x$, $\sigma y$, $\sigma x^2$, $\sigma xy$
$\sigma x$ = \boxed{} $\sigma y$ = \boxed{} $\sigma x^2$ = \boxed{} $\sigma xy$ = \boxed{}

c.) find the slope and the y-intercept of the best fit regression line. (round to 2 decimal places on slope
and y-int)
$y = mx + b$
$y$ = \boxed{}x + \boxed{}

d.) based on your answer from part c, what would you estimate the overall average is for students who are
absent 3 days in a semester?
\boxed{} round to nearest %

Explanation:

Part a)

As the number of absences (\(x\)) increases (from 0 to 6), the overall grade (\(y\)) decreases (from 90 to 45). In a negative correlation, as one variable increases, the other decreases. So the data has a negative correlation.

Step1: Calculate \(\sum x\)

Sum the values of \(x\): \(0 + 2 + 5 + 6 = 13\)

Step2: Calculate \(\sum y\)

Sum the values of \(y\): \(90 + 80 + 70 + 45 = 285\)

Step3: Calculate \(\sum x^2\)

Square each \(x\) and sum: \(0^2 + 2^2 + 5^2 + 6^2 = 0 + 4 + 25 + 36 = 65\)

Step4: Calculate \(\sum xy\)

Multiply each \(x\) and \(y\) and sum: \((0\times90)+(2\times80)+(5\times70)+(6\times45)=0 + 160 + 350 + 270 = 780\)

The formula for the slope \(m\) of the regression line is \(m=\frac{n\sum xy-\sum x\sum y}{n\sum x^2 - (\sum x)^2}\), and the y - intercept \(b=\frac{\sum y - m\sum x}{n}\), where \(n = 4\) (number of data points).

Step1: Calculate the slope \(m\)

First, substitute \(n = 4\), \(\sum x = 13\), \(\sum y = 285\), \(\sum xy = 780\), \(\sum x^2 = 65\) into the slope formula:

$$
LATEXBLOCK0
$$

Step2: Calculate the y - intercept \(b\)

Substitute \(m\approx - 6.43\), \(\sum x = 13\), \(\sum y = 285\), \(n = 4\) into the y - intercept formula:

$$
LATEXBLOCK1
$$

Answer:

A. Negative

Part b)