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8) Using the following data, an SAT Test Score is predicted based on how a student performed on a standardized Math and English Test: SAT Test Score 900 1100 875 925 790 800 975 Math 275 400 199 325 390 245 300 English 400 290 375 350 315 300 345 Is this a good regression model? If you wanted to use the student's gender in the model, how would you do it? What would the new regression equation be and is it better than the original model? 

          8) Using the following data, an SAT Test Score is predicted based on how a student performed on a
standardized Math and English Test:
SAT Test Score 900 1100 875 925 790 800 975
Math	275 400 199 325 390 245 300
English	400 290 375 350 315 300 345
Is this a good regression model?
If you wanted to use the student's gender in the model, how would you do it? What would the new
regression equation be and is it better than the original model?
Show more…
8) Using the following data, an SAT Test Score is predicted based on how a student performed on a standardized Math and English Test: SAT Test Score 900 1100 875 925 790 800 975 Math 275 400 199 325 390 245 300 English 400 290 375 350 315 300 345 Is this a good regression model? If you wanted to use the student's gender in the model, how would you do it? What would the new regression equation be and is it better than the original model?

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Using the following data, an SAT Test Score is predicted based on how a student performed on a standardized Math and English Test: SAT Test Score Math English 900 1100 875 925 790 800 975 275 400 199 325 390 245 300 400 290 375 350 315 300 345 Is this a good regression model? If you wanted to use the student's gender in the model, how would you do it? What would the new regression equation be and is it better than the original model?
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Transcript

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00:01 So first we want to find a description of this relationship.
00:03 So i would say that this has a positive, moderately strong, linear relationship.
00:14 It definitely doesn't fit it perfectly.
00:18 There is variability around it, but it does have that positive trend and in the linear fashion.
00:24 Part b said, are there any students whose score do not fit the overall pattern? and so when we look at the graph, we can see that there are, it looks like there's an upper outlier that's maybe at, maybe at about a point of 480 maybe and 800.
00:44 So it looks like there might be an outlier at maybe about 480 and 800, that that person seems to be kind of high compared to the rest of the values.
00:55 Part c says, for these data, the r value is equal to .685, and that means that as we have the verbal score increasing, that it appears as though the math score also seems decreased.
01:12 But again, it is only moderately strong.
01:16 Letter d says that the verbal scores average 596 .2, or excuse me, .3 with a standard deviation of 99 .5.
01:27 And the math scores, which we'll call that y, has a mean score of 612 .2 with a standard deviation of 96 .1, and we want to find the equation of the regression line.
01:40 And so we know we need to find the r, excuse me, the slope first so that b sub 1 will equal the r value, which is that .685 times the standard deviation of the y, divided by the standard deviation of the x.
01:57 And so .685 times that 96 .1 divided by 99 .5 gives us a value of .661, and i'll just call it 6 -0, although i'm going to store that in my calculator.
02:12 And then the b sub 0 value will be the y bar minus the slope times the x bar, which is that 596 .3.
02:25 And so 612 .2 minus that value that i just stored, the slope, times that 596 .3 gives us a y intercept of 217 .692.
02:41 And once again, i'm going to store that value in my calculator.
02:45 Now part e asks us to describe the relationship for the slope, or what does that slope mean? we know that's the change in the math over the change in the verbal score.
03:04 And so as the verbal score increases by 1, we anticipate an increase in the math score by .662...
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