What is the value of the Y-intercept of the least-squares regression line from this data? Round you answer to at least two decimal places. I add all the y up's and came up with 2714.4. Then is says the least-squares regression line for these data has a slope of approximately 0.56. the x data comes up 2686. Then what is the sample correlation coefficient for these data? Have no idea how to even start. Pleae help me if you can
To find the value of the Y-intercept of the least-squares regression line, you need the slope of the line and the mean of the x and y values.
The slope of the least-squares regression line is given as 0.56 in the information you provided. You also indicated that the sum of the y values is 2714.4, and the sum of the x values is 2686.
To find the Y-intercept, you can use the formula for the equation of a straight line: y = mx + b, where m is the slope and b is the Y-intercept.
To calculate the Y-intercept, you need to substitute the values given into the formula:
2714.4 = 0.56 * 2686 + b
Now, solve for b:
b = 2714.4 - (0.56 * 2686)
Calculating this, you get:
b ≈ 2714.4 - 1501.76
b ≈ 1212.64
Therefore, the Y-intercept of the least-squares regression line is approximately 1212.64.
To find the sample correlation coefficient, you can use the formula:
r = (nΣxy - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2) * (nΣy^2 - (Σy)^2))
In this formula, Σ represents the sum and n represents the number of data points.
You have the sum of the x and y values (Σx and Σy), the sum of the product of x and y values (Σxy), and the sum of the squares of x and y values (Σx^2 and Σy^2). However, I don't have the number of data points (n) or the individual x and y values to calculate the correlation coefficient.
If you could provide the remaining information, I would be able to help you find the sample correlation coefficient for these data.