MHB Does the entrance test score determine the final exam score?

[nycmathdad]

The table shows the mathematics entrance test scores x and the final examination scores y in an algebra course for a sample of 10 students.

x...22 29 35 40 44 48 53 58 65 76
y...53 74 57 66 79 90 76 93 83 99

(a) Sketch a scatter plot of the data.

(b) Find the entrance test score of any student with a final exam score in the 80s.

(c) Does a higher entrance test score imply a higher final exam score? Explain.

Let me see.

Part (a) is just plotting points on the xy-plane.

Part (b)
The entrance score is 65 as shown in the table above for the point (65, 83).

Part (c)
A higher entrance score does not imply a higher final exam score. The table shows how entrance scores and final exam scores fluctuate. The point (76, 99) shows that a high entrance score led to a high final exam score but the case is different for (48, 90). A low entrance score of 48 led to a high final exam score of 90. Many factors lead to this fluctuation in terms of entrance scores versus final exam scores.

 

[Prove It]

This question is poorly worded, but I expect you are supposed to get a Least Squares Regression Line, so that you can use the equation to answer part (b) and determine if there is a trend in part (c).

 

[nycmathdad]

This question is poorly worded, but I expect you are supposed to get a Least Squares Regression Line, so that you can use the equation to answer part (b) and determine if there is a trend in part (c).

Ok. I will research this problem online.

 

[HOI]

The data are given in order increasing entrance score. The corresponding final scores are:
53 74 57 66 79 90 76 93 83 99
The scores increase from
53 to 75, from 57 to 66, from 66 to 76, from 76 to 989, and from 83 to 99, 5 times.
The scores deceas3 from
74 to 57 and from 93 to 83, 2 times,

While not always increasing the data are, overall, increasing.