Disclaimer: this is directly related to a homework problem. The example I am giving is based off the homework problem (because I am more interested in how to solve it than in what the answer is).
- Number of people surveyed: 50
- Sum of x values: 1500
- Sum of y values: 500
- Point on least squares regression line: (5, 0)
Problem: What is the least squares regression line's predicted y-value at x = 25?
What I've done so far: Based off of the count and sum, I was able to get the mean for x (30) and for y (10). However, it is here that I get stuck. I only know how to calculate the least square regression line (LSRL) when given Sx and Sy (std dev of x and y). But I cannot calculate the std dev of either without having the actual data points!
After some thought, I realized that since I know one point of the LSRL, I could figure out any other point along the line if I knew the slope. But then I realized I do not know how to calculate the slope without first knowing Sx and Sy.
I have reached the conclusion that there are only three possible reasons I do not yet have the answer to this question...
- There is a way to calculate the std dev from this data, but I don't know it.
- There is another way to calculate the second point without using std dev, but I don't know it.
- My professor forgot to give us the data table, and without that I am unable to solve this.