There is often thought to be a relationship between a person's educational attainment and the number of children he or she has. The hypothesis is that as one's educational level increases, he or she has fewer children. Let us suppose that we have a sample of 1000 people from a country. The sample has a mean of 2 children with a variance of 2.02. The mean for years of schooling is 9.8 with a variance of 14.65. The covariance is -5.23. Consider number of children the dependent variable.
Write the formula to calculate the slope (b): b = ____________
Calculate the slope:
Explain the meaning of this value:
Write the formula to calculate the intercept (a): a = ____________
Calculate the intercept:
Explain the meaning of this value:
If the R^2 is .4286, explain what this means:
Write the formula to calculate the slope (b): b = ____________
Calculate the slope:
Explain the meaning of this value:
Write the formula to calculate the intercept (a): a = ____________
Calculate the intercept:
Explain the meaning of this value:
If the R^2 is .4286, explain what this means:
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Kelly -
The slope of a regression line (b) equals the correlation coefficient times the standard deviation of the dependent variable divided by the standard deviation of the independent variable:
Since they don't provide the correlation coefficient, it can be calculated by dividing the covariance by the product of the standard deviations of the dependent and independent variables.
correlation coefficient = -5.23 / [(sqrt( 2.02) sqrt(14.65)] = -0.9614
b = -0.9614 sqrt (2.02) / sqrt (14.65) = -0.357
The negative makes sense since we are expecting as schooling increases number of children will decrease, agree?
What does it mean? For every 1 unit increase in schooling, number of children decreases by 0.357
In order to solve for the y-intercept (a), solve for it in this equation:
y-mean = b(x-mean) + a
2 = -0.357(9.8) + a
a = 5.5
The intercept happens when number of years of schooling is 0, so if you have no schooling, then the expected number of children is 5.5.
R^2 of .4286 means the independent variable explains 42.86% of the variation in the dependent variable.
Hope that helped
The slope of a regression line (b) equals the correlation coefficient times the standard deviation of the dependent variable divided by the standard deviation of the independent variable:
Since they don't provide the correlation coefficient, it can be calculated by dividing the covariance by the product of the standard deviations of the dependent and independent variables.
correlation coefficient = -5.23 / [(sqrt( 2.02) sqrt(14.65)] = -0.9614
b = -0.9614 sqrt (2.02) / sqrt (14.65) = -0.357
The negative makes sense since we are expecting as schooling increases number of children will decrease, agree?
What does it mean? For every 1 unit increase in schooling, number of children decreases by 0.357
In order to solve for the y-intercept (a), solve for it in this equation:
y-mean = b(x-mean) + a
2 = -0.357(9.8) + a
a = 5.5
The intercept happens when number of years of schooling is 0, so if you have no schooling, then the expected number of children is 5.5.
R^2 of .4286 means the independent variable explains 42.86% of the variation in the dependent variable.
Hope that helped