Topic 7

Question 1

What is the intention of a simple linear regression?

Answer 1

• to develop a model that can be used to predict the value of Y, given X

Question 2

To compute?

Answer 2

• the general format of the relationship between two variables, denoted as Y and X

Question 3

To compute?

Answer 3

• the estimated model (using Excel/PHStat) is generally presented as:
• where values b₀ and b₁ are taken from the output and provides the estimated coefficients

Question 4

What is β₀?

Answer 4

• the intercept term, which is estimated using the value of b₀
• denotes that the expected value of Y is X is equal to zero

Question 5

What is β₁?

Answer 5

• the slope term which is estimated using the value of b₁
• this gives us the marginal change in the expected value of Y for a unit change in X
• if β₁ is positive, then the line slopes upward
• if β₁ is negative, then the line slopes down

(that is, increasing X by one unit results in Y decreasing)

Question 6

What does the standard error of the estimate do?

Answer 6

• estimates the standard deviation of the errors, or, equivalently, the standard deviation of the possible Y-values associated with any particular X-value

Question 7

What does the coefficient of determination do?

Answer 7

• provides the proportion of the variation in Y that is explained by the linear model containing X as an explanatory variable

Question 8

What do we use the estimated model for?

Answer 8

• to predict the value of Y, given X
• need to substitute the value of X with the correct units used to the estimated equation

Question 9

How can we test the significance of the relationship between Y and X?

Answer 9

• using a t-test

Question 10

What are the dependent and independent variables for this study? State and report the regression model.

Answer 10

Question 11

What information does the coefficient b₁ in the regression equation provide about the relationship between examination grade and study hours?

Answer 11

Question 12

Test the null hypothesis that the slope of the regression line is zero.

Use 5% level of significance.

Interpret the result of your test.

Answer 12

Question 13

Test the null hypothesis that the true regression coefficient is less than or equal to zero.

Use 5% level of significance.

Interpret the result of your test.

Answer 13

Question 14

Estimate the examination grade of a student who devoted 30hr of study to course preparation.

Answer 14

Question 15

Report and interpret the value of the coefficient of determination.

Answer 15

The coefficient of determination, R² = 0.74.

This implies that 74% of the variation in examination grade can be explained by the number.

Question 16

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Question 17

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Question 18

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Question 19

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Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

Answer 29