# Simple Linear Regression

## Presentation on theme: "Simple Linear Regression"— Presentation transcript:

Simple Linear Regression

Anxiety and Performance
To measure the relationship between anxiety level and test performance, an educational psychologist obtains a random sample of n = 6 college students from an introductory statistics course. The students are asked to come to the Educational Research and Evaluation Laboratory (EREL) 15 minutes before the final exam. In the lab, the researcher records the physiological measures of anxiety (heart rate, skin resistance, blood pressure, and so on) for each participant. Following the final, the researcher obtained the exam score for each participant. Table 1 summarizes the data.

Table 1 Student Anxiety Rating Exam Score A 5 80 B 2 88 C 7 D 79 E 4
86 F 85 Mean 83 S.D. 1.90 3.79

Scatterplot B E F A C D Student Anxiety Rating Exam Score A 5 80 B 2
88 C 7 D 79 E 4 86 F 85 B E F A C D

Slope Calculation

Slope Calculation Student Anxiety Rating (X-`X) (X-`X)2 Exam Score
(Y-`Y) (Y-`Y)2 (X-`X)(Y-`Y) A 5 80 -3 9 B 2 88 25 -15 C 7 4 -6 D 79 -4 16 -8 E -1 1 86 3 F 85 Mean 18 83 72 -32

Slope Calculation Student Anxiety Rating X 2 Exam Score XY A 5 25 80
400 B 2 4 88 176 C 7 49 560 D 79 553 E 16 86 344 F 85 425 S = 30 168 498 2458 (S)2 = 900

Slope Calculation Student Anxiety Rating Exam Score A 5 80 B 2 88 C 7
79 E 4 86 F 85 Mean 83 S.D. 1.90 3.79 rxy = -0.89

Intercept Calculation
Student Anxiety Rating Exam Score A 5 80 B 2 88 C 7 D 79 E 4 86 F 85 Mean 83 S.D. 1.90 3.79 rxy = -0.89 by∙x = -1.78

Regression Line Regression Equation for X = 4 for X = 6

Scatterplot (4, 84.78) (6, 81.22)

Coefficient of Determination - r 2xy
B E F DATA Student Anxiety Rating Exam Score Predicted Score A 5 80 83.00 B 2 88 88.34 C 7 79.44 D 79 E 4 86 84.78 F 85 A C D

Coefficient of Determination - r 2xy
Error between Y and `Y Error between Y and ^Y Student Anxiety Rating Exam Score ^Y (Y-`Y) (Y-`Y)2 (Y- ^Y) (Y- ^Y)2 A 5 80 83.00 -3.00 9.00 B 2 88 88.34 5.00 25.00 -0.34 0.12 C 7 79.44 0.56 0.31 D 79 -4.00 16.00 -0.44 0.19 E 4 86 84.78 3.00 1.22 1.49 F 85 2.00 4.00 Mean 83 0.00 72.00 15.11 S.D. 1.90 3.79 0.21 rxy = -0.89 r 2xy = 0.79