The scatter diagram of midterm scores and final scores in a large class is football shaped. For about 80% of the students, the regression estimate of final score based on midterm score is correct to within 15 points. For about 95% of the students, the regression estimate of final score based on midterm score is correct to within how many points?
It has to be 21
why 21?
22.95
80% is between -1.2815 and 1.2815 in standard units
90% is between -1.96 and 1.96
15/r.m.s. error = 1.2815
score/r.m.s. error = 1.96
=> score = 15*1.96/1.2815
Now, when rounding 1.2815 to either 1.281 or 1.282 you'll get slightly different result
To determine the number of points within which the regression estimate of final score based on midterm score is correct for about 95% of the students, we need to understand the concept of standard deviation.
Standard deviation is a measure of the spread or dispersion of a set of data values. In this case, it would represent the average amount by which the actual final scores deviate from the regression estimate based on their corresponding midterm scores.
The term "football-shaped scatter diagram" typically suggests a bell-shaped distribution, which follows a normal distribution pattern. In a normal distribution, around 68% of the data falls within one standard deviation, while approximately 95% falls within two standard deviations.
From the given information, we know that for about 80% of the students, the regression estimate of final score based on midterm score is correct within 15 points. This means that the standard deviation is approximately 15 points.
To find the range within which the regression estimate is correct for about 95% of the students, we can calculate two standard deviations: 2 * 15 = 30 points.
Therefore, for about 95% of the students, the regression estimate of the final score based on the midterm score will be correct within 30 points.