Question

1. List the strength and direction of the following correlations: r = .02 r = .53 r = -.89 2. Describe the difference between correlation and prediction (regression) analysis approaches? 3a. A regression model predicting the yearly salary (Y) for a teacher is predicted by years of experience(X). The analysis produces a constant of 38,000 and an intercept (slope) of 1,500. According to the model, what would be the salary of a teacher who has worked for 12 years? 3b. Additional variables are added to improve the model predicting annual teacher salary (Y). The model now includes years of experience (X1), number of awards (X2), and age (X3). The analysis produces a constant of 38,000, and the following slopes (x1 = 1,500, x2 = 5,000, x3 = .055). What would be the salary of a teacher who has worked for 5 years, won 2 awards, and is 27-years-old?

Answer 1

List the strength and direction of the following correlations: r = .02 r = .53 r = -.89 2. Describe the difference between correlation and prediction (regression) analysis approaches

r = 0.02 : 0 < r< 0.5 and positive so there is weak correlation

r = 0.53 : Closer to 0.5, so there is moderate positive correlation

r = -0.89 : r < 0 and closer to -1. There is strong negative correlation.

The higher the correlation, the higher the chances to get better predictions. So here the data with r = -0.89 should use the regression approach.

3a. A regression model predicting the yearly salary (Y) for a teacher is predicted by years of experience(X). The analysis produces a constant of 38,000 and an intercept (slope) of 1,500. According to the model, what would be the salary of a teacher who has worked for 12 years?

Regression eq of Y on X

Slope b = 1500

intercept a = 38000

Therefore y = 38000+ 1500 x

So when there is 12 years of experience we have x = 12

y = 38000+ 1500* 12

y = 56000

The salary is predicted to be 56000.

3b. Additional variables are added to improve the model predicting annual teacher salary (Y). The model now includes years of experience (X1), number of awards (X2), and age (X3). The analysis produces a constant of 38,000, and the following slopes (x1 = 1,500, x2 = 5,000, x3 = .055). What would be the salary of a teacher who has worked for 5 years, won 2 awards, and is 27-years-old?

The previous model was one factor linear reg. This is multifactor models. This will have one constant but many slopes

y = a + b₁x₁+ b₂x₂+ b₃x₂​​​​​​3+ b₄x₄+ ........

Here we have 3 factors

Constant a = 38000

Experience b₁= 1500

Awards b₂ = 5000

Age b₃ = 0.055

y = 38000 + 1500x1 + 5000x2 + 0.055x3

For each factor we have 'x' values

x₁ = 5 x₂ = 2 x₃ = 27

We sub

y = 38000 + 1500* 5 + 5000 *2 + 0.055 * 27

y = 55501.49