A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y)
are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 69.
1 answer:
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Answer <u>(assuming it can be in slope-intercept format)</u>:
Step-by-step explanation:
When knowing the y-intercept of a line and its slope, we can write an equation representing it in slope-intercept form, or .
1) First, find the slope of the equation. Use the slope formula, , to find the slope. Substitute the x and y values of the given points into the formula and simplify:
Thus, the slope is .
2) Usually, we would have to use one of the given points and the slope to put the equation in point-slope form. However, notice that the point (0,7) has an x-value of 0. All points on the y-axis have an x-value of 0, thus (0,7) must be the y-intercept of the line. Now that we know the slope of the line and its y-intercept, we can already write the equation in slope-intercept format, represented by the equation . Substitute
and
for real values.
Since represents the slope, substitute
in its place in the equation. Since
represents the y-intercept, substitute 7 in its place. This gives the following equation and answer: