Answers:
- 3. E) -0.8
- 4. True
- 5. True
- 6. True
- 7. D) 17.62%
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Explanations:
3. We have negative correlation because the regression line is going downhill (move from left to right). The points are fairly close to the same regression line, so I'd say we have either moderate or fairly strong negative correlation. That means r is fairly close to -1. It's not -1 exactly since that would have to mean all points are on the same line.
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4. Negative correlation goes with negative r values. Refer to problem 3. Positive correlation goes to positive r values. The r value will most likely not equal the slope value, but they share the same sign.
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5. If r is close to +1, then we have fairly strong positive linear correlation. If r is close to -1, then we have fairly strong negative linear correlation. If r = 0 or close to it, then we should use some other kind of regression tool. Or perhaps the data points are simply randomly scattered about and they have no pattern at all.
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6. Refer to problem 5.
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7. Plug in x = 15 and you should find that y = -0.632(15)+27.1 = 17.62, which means that the estimated tip is roughly 17.62% of the bill.
The total cost is $41.85
Amount Saved = 45 x 7 / 100
Amount Saved = 315 / 100
Amount Saved = $3.15 (answer).
In other words, a 7% discount for a item with original price of $45 is equal to $3.15 (Amount Saved).
Note that to find the amount saved, just multiply it by the percentage and divide by 100.
