At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (within a range). thinking about how the person could have predicted your weight fairly accurately (despite the fact that she did not know about your "heavy bones"), you think about how this could have been accomplished. you remember that medical charts for children contain 5%, 25%, 50%, 75% and 95% lines for a weight/height relationship and decide to conduct an experiment with 110 of your peers. you collect the data and calculate the following sums: where the height is measured in inches and weight in pounds.

(a) calculate the slope and intercept of the regression.
(b) find the regression r2.

a)Slope:

Intercept:

b)  

And the determination coeffecient is  

Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"    

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.  

n=110,  

Part a

The slope is given by this formula:

If we replace we got:

We can find the intercept with the following formula

We can find the average for x and y like this:

And replacing we got:

Part b

In order to calculate the correlation coefficient we can use this formula:  

For our case we have this:  

n=110,  

So we can find the correlation coefficient replacing like this:

And the determination coeffecient is  

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right