Consider the exam data below.
Algebra score:
20
35
13
29
40
23
Calculus score:
41
69
34
72
86
58
Use your calculator to find the regression line for this data, and graph it on your scatterplot.
b. Interpret the slope and intercepts of this line in the context of the problem.
c. According to your model, what score on the Calculus exam should a student expect if they earned a score of 31 on their Algebra II exam?
To find the regression line for this data, we'll use a graphing calculator. Here's how you can do it:
1. Input the Algebra scores in a list, say L1, on your calculator.
2. Input the Calculus scores in another list, say L2.
3. Go to the statistics or regression menu on your calculator. Look for an option like "Linear Regression" or "LinReg."
4. Enter L1 as the x-values and L2 as the y-values.
5. Calculate the regression line. It will give you the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept.
Now, let's interpret the slope and intercepts in the context of the problem:
The slope (m) of the regression line represents the expected change in the Calculus score for each unit increase in the Algebra score. In this case, if the Algebra score increases by 1, the Calculus score is expected to increase by the slope value.
The y-intercept (b) represents the predicted Calculus score when the Algebra score is zero. However, in this case, it doesn't make sense to interpret the y-intercept because an Algebra score of zero is not possible within the given data. So, we can ignore the interpretation of the y-intercept in this context.
Finally, to find the expected Calculus score for an Algebra score of 31:
1. Substitute the Algebra score (31) into the regression equation, using the slope and y-intercept you obtained earlier.
2. Solve the equation to get the predicted Calculus score for an Algebra score of 31.
Remember that the regression line is an approximation based on the given data, and the predicted value may not always be exact.
By following these steps, you should be able to find the regression line, interpret the slope and intercepts, and predict the Calculus score for a given Algebra score.