Chapter 10. Lecture 2 Section: 10.3. We analyzed paired data with the goal of determining whether there
1. We are investigating only linear relationships.
2. For each x-value, y is a random variable having a normal distribution. All of these y distributions have the same variance. Also, for a given value of x, the distribution of y-values has a mean that lies on the regression line. Results are not seriously affected if departures from normal distributions and equal variances are not too extreme.
Regression equations can be helpful when used for predicting the value of one variable, given some particular value of the other variable. If the regression line fits the data quite well, then it makes sense to use its equation for predictions, provided that we don’t go beyond the scope of the available values. However, we should use the equation of the regression line only if r indicates that there is a linear
In the absence of a linear correlation, we shouldnot usethe regression equation for projecting or predicting; instead, our best estimate of the second variable is simply its sample mean. Which will be y.
Thus our guide lines in predicting a value of y based on some given value of x are:
1. If there is not a linear correlation, the best predicted y-value is y .
2. If there is a linear correlation, the best predicted y-value is found
by substituting the x-value into the regression equation.
The accompanying table lists monthly income and their food expenditures for the month of December.
FoodEx versus income
The regression equation is
FoodEx = 151 + 0.252 income
Predictor Coef SE Coef T P
Constant 150.7 217.4 0.69 0.519
income 0.25246 0.03788 6.66 0.001
S = 159.508 R-Sq = 89.9% R-Sq(adj) = 87.9%
Compute the regression equation and find the arm length if the neck size is 16.0.
2. Compute the regression equation and find the GPA of a student if their SAT score is 1000.
4. The accompanying table lists weights in pounds of paper discarded by a sample of households, along with the size of the household.
Paper: 2.41 7.57 9.55 8.82 8.72 6.96 6.83 11.42
HSize : 2 3 3 6 4 2 1 5
What is the best predicted size of a household that discards 10lbs. of paper.
5. The following is the age and the corresponding blood pressure of 10 subjects randomly selected subjects from a large city
Estimate the blood pressure of some one who is 40 years of age.
6. A study was conducted to investigate the relationship between age (in years) and BAC (blood alcohol concentration) measured when convicted DWI (driving while intoxicated) jail inmates were first arrested. What is the best predicted BAC of a person who is 22 years of age who has been convicted and jailed for a DWI?