Answer:
y = 72.35 + 2.95x
Explanations:
Let the number of tutorials attended be represented by x
Let the semester grade be represented by y
x = { 9, 4, 0, 0, 6, 1}
y = {99, 91, 63, 78, 85, 77}
Calculate the mean of x
[tex]\begin{gathered} \bar{X}\text{ = }\frac{9+4+0+0+0+6+1}{5} \\ \bar{X}\text{ =}\frac{20}{6} \\ \bar{X}\text{ =}3.33 \end{gathered}[/tex]
Calculate the mean of y
[tex]\begin{gathered} \bar{Y}\text{ =}\frac{99+91+63+78+85+77}{6} \\ \bar{Y}\text{ = }\frac{493}{6} \\ \bar{Y}\text{ =}82.17 \end{gathered}[/tex][tex]m\text{ = }\frac{\sum ^n_{i\mathop=1}(x_i-\bar{X}\text{ )(y}_i-\bar{Y)}\text{ }}{\sum ^n_{i\mathop{=}1}(x_i-\bar{X}\text{ )}^2}[/tex][tex]\begin{gathered} m\text{ = }\frac{(9-3.33)(99-82.17)+(4-3.33)(91-82.17)+(0-3.33)(63-82.17)+(0-3.33)(78-82.17)+(6-3.33)(85-82.17)+(1-3.33)(77-82.17)}{\mleft(9-3.33\mright)^2+\mleft(4-3.33\mright)^2+(0-3.33)^2+(0-3.33)^2+(6-3.33)^2+(1-3.33)^2} \\ \text{m = }\frac{198.67}{^{}67.33} \\ \text{m = }2.95 \end{gathered}[/tex]
Calculate the y-intercept using the formula below:
[tex]\begin{gathered} b\text{ = }\bar{Y}-m\bar{X}\text{ } \\ \text{b = 82.17-2.95(3.33)} \\ \text{b = 82.17-}9.82 \\ b\text{ = }72.35 \end{gathered}[/tex]
The equation of a line is:
y = mx + b
Substitute m = 2.95 and b = 72.35 into the equation of a line given above:
y = 2.95x + 72.35
