Chapter 1. Testing the Hypothesis of No Linear Relationship

Correct. If there is no linear relationship between X and Y, then X cannot be used to predict Y with a linear model.

Incorrect. If there is no linear relationship between X and Y, then X cannot be used to predict Y with a linear model.

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Correct. If every value of X predicts the same value for Y, then slope is zero.

Incorrect. If every value of X predicts the same value for Y, then slope is zero.

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Correct. The hypothesis H₀: β = 0 symbolically represents “There is no relationship between X and Y.”

Incorrect. The hypothesis H₀: β = 0 symbolically represents “There is no relationship between X and Y.”

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Correct. We can say that X can be used to predict Y with the equation \( \widehat{y} \) = a + bx whenever we reject the null hypothesis.

Incorrect. We can say that X can be used to predict Y with the equation \( \widehat{y} \) = a + bx whenever we reject the null hypothesis.

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Correct. We want the alternative to be H_a: β > 0 because we believe that as a tree’s diameter increases, its volume of wood also increases. It doesn’t make sense to believe that volume decreases as diameter increases.

Incorrect. We want the alternative to be H_a: β > 0 because we believe that as a tree’s diameter increases, its volume of wood also increases. It doesn’t make sense to believe that volume decreases as diameter increases.

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Correct. Since the relationship is clearly linear and very strong, we will probably reject H₀.

Incorrect. Since the relationship is clearly linear and very strong, we will probably reject H₀.

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Correct. Slope tells us the average change in Y for every one unit increase in X. Since X is diameter in inches, a one unit increase is a one inch increase. So, slope tells us that volume increases by 5.07 hundred board feet on average as diameter increases by one inch.

Incorrect. Slope tells us the average change in Y for every one unit increase in X. Since X is diameter in inches, a one unit increase is a one inch increase. So, slope tells us that volume increases by 5.07 hundred board feet on average as diameter increases by one inch.

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Correct. No megaphone pattern is visible so constant standard deviation condition is ok.

Incorrect. No megaphone pattern is visible so constant standard deviation condition is ok.

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Correct. No smile or frown pattern in the residual plot so linearity condition is ok.

Incorrect. No smile or frown pattern in the residual plot so linearity condition is ok.

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Correct. With no outlier in the histogram of residuals, the Normality condition is ok.

Incorrect. With no outlier in the histogram of residuals, the Normality condition is ok.

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Correct. Degrees of freedom = n – 2 = 31 – 2 = 29.

Incorrect. Degrees of freedom = n – 2 = 31 – 2 = 29.

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Correct. Since P-value < 0.0001 is less than α = 0.05, we can reject H₀.

Incorrect. Since P-value < 0.0001 is less than α = 0.05, we can reject H₀.

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Correct. Since there is a linear relationship between diameter and volume of wood, we can use the diameter of a tree to predict its volume of wood.

Incorrect. Since there is a linear relationship between diameter and volume of wood, we can use the diameter of a tree to predict its volume of wood.

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