Key Terms
Example
Y = 25 + 15x (flat fee of $25, plus $15 per hour)
Only when
1. The scatter plot shows a linear pattern 2.
Also
B = r(sy / sx) Where r = correlation coefficient, sy = standard deviation of y, sx = standard deviation of x.
Measures
1. STRENGTH of the linear relationship between x and y 2.
RANGE
-1 <= r <= 1. Always.
Interpretation
About 44% of the variation in final exam scores can be explained by the variation in third exam scores, using the regres
Two values matter together
R AND n (sample size).
Significance level
Alpha = 0.05 (standard for this course)
Degrees of freedom
Df = n - 2
Test statistic
T = r * sqrt(n-2) / sqrt(1 - r-squared) (Technology calculates this for you.)
EXAMPLE
R = 0.776, n = 6, df = 4, critical value = 0.811 -0.811 < 0.776 < 0.811, so r is NOT significant.
WHEN r IS SIGNIFICANT
You CAN use the regression line to model and predict y from x within the observed data range.
WHEN r IS NOT SIGNIFICANT
Do NOT use the regression line for prediction. It has no statistical basis.
Data
X values range from 65 to 75 (third exam scores) Equation: y-hat = -173.51 + 4.83x
Lower fence
308,750 - 510,375 = -201,625 Upper fence: 649,000 + 510,375 = 1,159,375