Question

A simple random sample of 6 paired values (x,y) yields the following statistical calculations: ∑x=46,∑y=130,Σ(x 2 )=394,Σ(y 2 )=3008,∑(xy)=981 1. Find n∑(xy)−(∑x)(∑y)= 2. Find n∑(x 2 )−(∑x) 2= 3. Find n∑(y 2 )−(∑y) 2 = 4 . Find the linear correlation coefficient r= ____________

Answer 1

Based on the provided data, we are given that:

n = 6
∑x=46
∑y=130
∑(x^2)=394
∑(y^2)=3008
∑(Xu)=981

We can start with calculating the specific quantities:

1. First, we find n∑(Xu)−(∑x)(∑y). By substituting in the given values, we get 6*981 - 46*130 = -94.

2. Next, we calculate n∑(x 2 )−(∑x) 2. Substituting the given values, that gives you 6*394 - 46^2 = 248.

3. For n∑(y 2 )−(∑y) 2, plug in the given numbers to get 6*3008 - 130^2 = 1148.

4. Finally, for the calculation of the linear correlation coefficient (r), the formula is

r = [n∑(Xu)−(∑x)(∑y)] / √([n∑(x^2)−(∑x)^2]*[n∑(y^2)−(∑y)^2])

Substitute the results of the above three calculations into the formula, you have -94 / sqrt(248 * 1148) = -0.1762 (rounded to four decimal places).

So, here are the answers to the requested calculations:

1. n∑(XXY)−(∑x)(∑y) = -94
2. n∑(x 2 )−(∑x) 2 = 248
3. n∑(y 2 )−(∑y) 2 = 1148
4. Linear correlation coefficient, r = -0.1762