a mathematics teacher wanted to see the correlation between test scores and homework. the homework grade (x)…

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 68.\nhomework grade (x) test grade (y)\n57 62\n85 75\n80 76\n75 68\n87 89\n50 38\n58 45\n79 64\ncopy values for calculator\nopen statistics calculator\nanswer\nregression equation:\nfinal answer:

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 68.\nhomework grade (x) test grade (y)\n57 62\n85 75\n80 76\n75 68\n87 89\n50 38\n58 45\n79 64\ncopy values for calculator\nopen statistics calculator\nanswer\nregression equation:\nfinal answer:

Answer

Explanation:

Step1: Calculate sums

Let (n = 9) (number of data - points). Calculate (\sum x), (\sum y), (\sum x^{2}), (\sum xy): (\sum x=57 + 85+80 + 75+87+50+58+79 = 671) (\sum y=62 + 75+76+68+89+38+45+64 = 517) (\sum x^{2}=57^{2}+85^{2}+80^{2}+75^{2}+87^{2}+50^{2}+58^{2}+79^{2}=57^{2}+7225 + 6400+5625+7569+2500+3364+6241=44298) (\sum xy=(57\times62)+(85\times75)+(80\times76)+(75\times68)+(87\times89)+(50\times38)+(58\times45)+(79\times64)=3534+6375+6080+5100+7743+1900+2610+5056 = 42498)

Step2: Calculate slope (m)

The formula for the slope (m) of the regression line is (m=\frac{n\sum xy-\sum x\sum y}{n\sum x^{2}-(\sum x)^{2}}) [ \begin{align*} m&=\frac{9\times42498 - 671\times517}{9\times44298-(671)^{2}}\ &=\frac{382482-346907}{398682 - 450241}\ &=\frac{35575}{- 51559}\approx1.07 \end{align*} ]

Step3: Calculate y - intercept (b)

The formula for the y - intercept (b) is (b=\overline{y}-m\overline{x}), where (\overline{x}=\frac{\sum x}{n}=\frac{671}{9}\approx74.56) and (\overline{y}=\frac{\sum y}{n}=\frac{517}{9}\approx57.44) [ \begin{align*} b&=57.44-1.07\times74.56\ &=57.44 - 80.7892\ &\approx - 23.35 \end{align*} ]

The regression equation is (y = 1.07x-23.35)

Step4: Predict test grade

When (x = 68), (y=1.07\times68-23.35=72.76-23.35 = 49.41\approx49)

Answer:

Regression Equation: (y = 1.07x - 23.35) Final Answer: 49