Answers:
- 8) Choices E, F and G
- 9) r = -0.95
- 10) 0.9 (choice C)
- 11) Choice C. y1 = mx1+b
- 12) Choice B. Slope
- 13) Choice C. y intercept
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Explanations:
8) Positive r values always go with positive regression slopes. The r value will likely not equal the slope, but they share the same sign.
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9) The data set isn't given so I'm not sure. But it seems like your teacher just wants to know a hypothetical situation in which r value will produce the best fit. That would be r = -0.95 since we're the furthest from zero. The closer you are to r = 1 or r = -1, the better the fit.
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10) The blue regression line, aka line of best fit, is fairly close to all of the data points. Also, the blue line has a positive slope. This means r is fairly close to 1. So that's why we go with r = 0.9
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11) The general equation is y = mx+b. We simply replace x,y with x1,y1.
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12) When considering y = mx+b, the m is the slope. I'm not entirely sure where the m comes from, but I've read some sources that say 'm' somehow represents 'mountain' which involves slopes. This could have simply been a memorization tool and not the actual reason why m was chosen to be the slope.
As an example, y = 2x+5 has slope 2.
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13) The b in y = mx+b is the y intercept. It's the initial value.
It always occurs when x = 0 since
y = mx+b
y = m*0+b
y = b
Meaning the point (0,b) is the location of the y intercept.
For example, y = 2x+5 has y intercept 5 located at the point (0,5).