TRUE OR FALSE
1. True or false: Scatterplots are constructed with the y variable on the horizontal axis and the x variable on the vertical axis.
2. True or false: The y intercept measures the strength of the linear relationship between two numerical variables.
FILL IN THE BLANK
3. The “hat” over the y in ˆy indicates that it is a(n) __________ of y.
4. We interpret the slope of the regression line as the estimated change in y per __________ increase in x.
SHORT ANSWER
5. Making predictions based on x-values that are beyond the range of the x-values in our data set is called what?
6. Values of r close to −1 indicate what type of relationship between the two variables?
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CALCULATIONS AND INTERPRETATIONS
High and Low Temperature. Use the following information for Exercises 7–14. The low (x) and high (y) temperatures (in degrees Fahrenheit) for a sample of eight cities are shown in the following table.
Low temperature | High temperature |
---|---|
0 | 24 |
10 | 32 |
10 | 38 |
20 | 36 |
20 | 44 |
30 | 45 |
30 | 53 |
40 | 59 |
40 | 65 |
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7. Construct a scatterplot of high temperature versus low temperature.
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8. Based on your scatterplot, would you characterize the linear relationship, if any, as positive or negative?
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9. Compute the regression equation of high temperature versus low temperature.
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10. Calculate the three sums of squares: SSR, SST, and SSE.
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11. Calculate s, the standard error of the estimate. What does this number mean?
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12. Calculate r2. Comment on how useful the low temperatures are in predicting the high temperatures.
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13. Use r2 to calculate and interpret the correlation coefficient.
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14. Find the prediction error for when the low temperature is zero.