Simple Linear Regression

Statistical Tests: Simple Linear Regression Page 1/3

A linear regression analysis of Birth Weight (grams) and Gestational Age (weeks) gave the following output.

Model	Beta Coefficient	95%CI	p-value
Gestational Age	96.56	14.41 to 178.72	0.02
Constant	-230.34	-3340.0 to 3180.30	0.39

Welcome to the "Simple Linear Regression" quiz. There are 6 questions to answer.

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Q1. Which of the following statements is NOT true regarding linear regression?

a)It identifies significant predictors for a continuous outcome variable. ✔ ✗

b)It predicts the outcome of a binary variable with continuous variables. ✔ ✗

c)It quantifies a relationship between two continuous variables. ✔ ✗

d)It models a linear relationship between two continuous variables. ✔ ✗

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The answer is b).

Q2. We have a regression equation where Y = 10X + 20, if X is 5.3 what is Y?

a)25.3 ✔ ✗

b)33 ✔ ✗

c)53 ✔ ✗

d)73 ✔ ✗

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The answer is d). We start with Y = 10X +20, replace X with 5.3, so we get Y=10*5.3 + 20 which becomes Y = 53+20 and then Y=73.

Q3. If the correlation coefficient output from linear regression is 0.64. How much of the variation of the Y axis variable is explained by the X axis variable?

a)64% ✔ ✗

b)8% ✔ ✗

c)41% ✔ ✗

d)32% ✔ ✗

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The answer is c). The variation is given by r², where r is the correlation coefficient. In this example r = .64 so r² = 0.64 *0.64 = 0.41 = 41%. So the X or independent variable explains 41% of the Y or dependent variable. In which case 59% of the variation is the Y variable is unexplained in this simple linear regression model.

Q4. What would be the Null hypothesis be for a linear regression model of Gestational Age (Independent variable) and Birth Weight (dependent variable)?

a) There is a positive linear relationship between Gestational Age and Birth Weight ✔ ✗

b)There is a negative linear relationship between Gestational Age and Birth ✔ ✗

c)There is no linear relationship between Gestational Age and Birth ✔ ✗

d)There is a linear relationship between Gestational Age and Birth which could be either positive or negative ✔ ✗

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The answer is c). Our Null hypothesis would state there no relationship between our independent and dependent variables. It is saying that the β, (beta coefficient) is zero. The Alternative Hypothesis would state that there is a relationship but would not specify the direction, so it could be a positive or negative linear relationship.

Q5. What does the following plot tell us about our regression model?

a)We will be unlikely to be able to predict the Dependent Variable using the Independent variable. ✔ ✗

b)The assumption of constant variance for the regression model has been violated. ✔ ✗

c)The assumption of constant variance for the regression model has not been violated. ✔ ✗

d)The assumption of Normality for the regression model has been violated. ✔ ✗

e)The assumption of Normality for the regression model has not been violated. ✔ ✗

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The answer is c). The plot of predicted value against residual for the Dependent variable is used to check the assumption of constant variance for the regression model. In the plot the data points are scattered randomly, there is no obvious trend so the assumption is met.

Q6. Calculate the predicted birth weight of a baby born at 40 weeks gestational age.

a)3632. ✔ ✗

b)3747. ✔ ✗

c)3862. ✔ ✗

d)3977. ✔ ✗

e)4092. ✔ ✗

Feedback:

The answer is a). The prediction equation is Birthweight = α + β * Gestational Age. α = -230.34; β = 96.56. So we have Birthweight = -230.34 + 96.56 * Gestational Age, which becomes: Birthweight = -230.34 + 96.56 * 40 Birthweight = - 230.34 + 3862.4 remember to subtract 230.34 - it is negative Birthweight = 3632

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