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Example Questions
Example Question #231 : Data Analysis
A school principal conducted a statistical experiment to determine the relationship between and the number of hours spent studying each week. In this study, the principal assigned the number of hours spent studying as the independent variable, and the was assigned as the dependent variable. The principal drew a line of best fit and found the to be . What does this mean?
Every studying increases a student's
A student who studied hours per week received an average of
Every week of studying increased a student's by
The average student is
A student who studied hours per week received an average of
The question tells us that the hours spent per week studying is the independent variable, or the , and the is the dependent variable, or the
The is when ; thus, when a student spends zero hours studying their average is
Example Question #2171 : Psat Mathematics
Mr. Miller conducted a statistical experiment to determine the relationship between final grades and the number of school days that his students missed. In this study, he assigned the number of missed school days as the independent variable, and the final grade was assigned as the dependent variable. Every student started the class with a , and based on class assignments, tests scores, etc. the students' final grade was determined. Mr. Miller found that for every one day missed, the students' grade dropped by . Based on this data, select the equation of the best fit line for this scenario.
The equation of the best fit line will be in slope intercept form:
The question tells us that days are the independent variable, or , and the dependent variable is the final class grade, or
Every students starts with a . If we think about a graph, then the start of the graph is when is equal to zero, which is the ; thus, the value of the equation should be
The final piece that we need is the slope, or value, which is associated with the number of days missed. Let's recall from the question that for every single day missed the students grade dropped by . "Drops" means that we are going to have a negative slope; thus, the slope for this scenario is the following:
If we put all of the pieces together, then the equation for the line of best fit is the following:
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