Slf-Esteem Scoresdepression Scores
Mean 3.43 15.78
StrdDev 0.75 10.34
The above chart contains the means and standard deviations for self-esteem scores and depression scores. Using this information and the most likely correlation coefficient obtained in Question 12 (-.76), what is the regression equation for this data?
a. y = -51.72-10.48x
b. y= -21.45 -1.65x
c. y = 51.72-10.48x
d. y= 21.45 -1.65x
To find the regression equation, we can start by using the formula:
y = b0 + b1x
where y is the dependent variable (depression scores), x is the independent variable (self-esteem scores), b0 is the y-intercept, and b1 is the slope of the regression line.
To calculate the values of b0 and b1, we need the mean values of self-esteem scores (x) and depression scores (y), as well as the correlation coefficient (r).
From the given information:
Mean of x (self-esteem scores) = 3.43
Mean of y (depression scores) = 15.78
The correlation coefficient (r) = -0.76
Now we can substitute these values into the formulas to find the slope (b1):
b1 = r * (standard deviation of y / standard deviation of x)
= -0.76 * (10.34 / 0.75)
= -10.48
Next, substitute the values of the means and the slope into the formula to find the y-intercept (b0):
b0 = mean of y - (b1 * mean of x)
= 15.78 - (-10.48 * 3.43)
= 51.72
Now we have the values for b0 and b1, so we can write the regression equation:
y = 51.72 - 10.48x
Comparing this with the given options, we can see that the correct answer is:
c. y = 51.72 - 10.48x