Question

A researcher want to know if there is a relationship between sleep and anxiety. The researcher randomly selected n = 5 participants and asked each to rate their sleep quality and anxiety level on a scale of 1 to 5. The data are below:

Sleep Anxiety
X Y

2 2
3 3
2 2
4 2
5 2

Calculate the Sum of Squares for X (SSₓ)

Answer 1

To calculate the Sum of Squares for X (SSₓ), calculate the mean of the X values and then subtract the mean from each X value, square the result, and add up all the squared differences.

Step-by-step explanation:

To calculate the Sum of Squares for X (SSₓ), we need to first calculate the mean of the X values. The mean can be found by adding up all the X values and dividing by the number of participants. In this case, the mean is:

(2 + 3 + 2 + 2 + 5) / 5 = 2.8

Next, we need to subtract the mean from each X value and square the result. Then, we add up all the squared differences to get the Sum of Squares for X:

(2-2.8)^2 + (3-2.8)^2 + (2-2.8)^2 + (2-2.8)^2 + (5-2.8)^2 = 8.8

Therefore, the Sum of Squares for X (SSₓ) is 8.8.