1. Simple Linear Regression and Correlation
Prepared by:
Paolo lorenzo Bautista

2. Simple Linear Regression
In SLR, we assume one dependent and one independent variable.
We try to predict the outcome/result of a dependent variable based on the independent variable
Example: The intelligence test scores of 12 college freshmen were obtained, and we try to find out if this has an effect on the freshmen’s chemistry grade.
ITS 65 50 55 70
Chem Grade 85 74 76 90 87 94 98 81 91
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3. Simple Linear Regression
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4. Simple Linear Regression
We wish to find a line of the form
y = a + bx
which will tell us the trend shown by the data.
Using PHStat, we have
y = x
Predict a freshman’s chemistry grade if his intelligence test score is 70.
What should a freshman’s intelligence test score be if he wants a grade of 90 for chemistry?
Provide an interpretation of the slope.
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5. Correlation Analysis
Measures the strength of relationships between two variables by means of a number called the correlation coefficient.
Also called the Pearson correlation coefficient.
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6. Correlation Analysis
Photo from wikipedia
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7. Correlation Analysis
Example: Find the correlation coefficient from our previous example.
r = indicating a strong positive linear relationship
Coefficient of Determination (r2) – the percentage of the variation in the dependent variable (Y) that can be explained by a linear relationship with the independent variable (X)
r2 = meaning 74.38% of the variation in chemistry grades is explained by a linear relationship with intelligence scores
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8. Correlation Analysis May require careful personal inspection
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9. Hypothesis Testing for Correlation
H1: ρ≠0 (significant linear association between X and Y)
t-test with n-2 degrees of freedom
Test statistic:
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10. Exercise
The following data show the amount of money 8 companies used for advertising, and the corresponding sales:
Advertising ($)
Sales ($) 40
385 20
400 25
395
365 30
475 50
440
490
420
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11. Exercise
Provide the estimated regression equation to predict sales given the amount spent on advertising.
Provide an interpretation of the slope.
What is the expected sales of a company if it spends $45 for advertising.
Compute the correlation coefficient. Interpret.
Compute the coefficient of determination. Interpret.
Test if there is a significant linear association between advertising and sales.
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