# Chapter 1. Least-squares regression line

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Stat Tutor
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1:49

### Question 1.1

Incorrect. Prediction error is also called “residual.”
Correct. Prediction error is also called “residual.”
Incorrect. Try again.
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### Question 1.2

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Incorrect. Residual is the vertical distance from a data point to the regression line.
Correct. Residual is the vertical distance from a data point to the regression line.
Incorrect. Try again.
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2:14

### Question 1.3

Incorrect. Because we want the best fit of the regression line to the data, we want the “smallest” sum of square residuals.
Correct. Because we want the best fit of the regression line to the data, we want the “smallest” sum of square residuals.
Incorrect. Try again.
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### Question 1.4

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Incorrect. We want the errors to be as small as possible.
Correct. We want the errors to be as small as possible.
Incorrect. Try again.
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2:34

### Question 1.5

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Incorrect. The smallest SSE given in the table is 55.78.
Correct. The smallest SSE given in the table is 55.78.
Incorrect. Try again.
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3:14

4:16

### Question 1.6

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Incorrect. Since $$b = r \frac{ s_{y} }{ s_{x} }$$, the value of slope, b, is computed using “r”.
Correct. Since $$b = r \frac{ s_{y} }{ s_{x} }$$, the value of slope, b, is computed using “r”.
Incorrect. Try again.
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### Question 1.7

Incorrect. $$a = \overline{y} - b \overline{x}$$, so you need the value of slope in order to compute y-intercept.
Correct. $$a = \overline{y} - b \overline{x}$$, so you need the value of slope in order to compute y-intercept.
Incorrect. Try again.
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6:15

### Question 1.8

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Incorrect. In the equation ŷ = 2.034 + 0.051x, y-intercept is 2.034.
Correct. In the equation ŷ = 2.034 + 0.051x, y-intercept is 2.034.
Incorrect. Try again.
2

### Question 1.9

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Incorrect. In a regression, slope tells us the average change in Y as X increases by one-unit. Thus, the question is basically asking, “What is the slope?” In the least squares equation: ŷ = 2.034 + 0.051x, slope is 0.051.
Correct. In a regression, slope tells us the average change in Y as X increases by one-unit. Thus, the question is basically asking, “What is the slope?” In the least squares equation: ŷ = 2.034 + 0.051x, slope is 0.051.
Incorrect. Try again.
2

6:55

### Question 1.10

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Incorrect. X is composite ACT score and ACT scores are measured in points. So, a one-unit increase in X is a one point increase in composite ACT score.
Correct. X is composite ACT score and ACT scores are measured in points. So, a one-unit increase in X is a one point increase in composite ACT score.
Incorrect. Try again.
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7:42

### Question 1.11

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Incorrect. Predicting a graduating GPA of 2.034 for a zero composite ACT score is ludicrous.
Correct. Predicting a graduating GPA of 2.034 for a zero composite ACT score is ludicrous.
Incorrect. Try again.
2

### Question 1.12

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Incorrect. Slope tells us the average increase in number of calories for a one gram increase in fat. In the regression line calories = 237.54 + 10.4 fat, slope = 10.4.
Correct. Slope tells us the average increase in number of calories for a one gram increase in fat. In the regression line calories = 237.54 + 10.4 fat, slope = 10.4.
Incorrect. Try again.
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