ai) y = 3.32673x + 86.32673
ii) r = 0.944502376
b) 179.5 cm
Explanation:
Regression equation model is in the form:
[tex]\begin{gathered} y\text{ = ax + b} \\ a\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]
To get the model that shows the relationship between x and y, we will use a regression calculator:
[tex]\begin{gathered} \text{The model is given by:} \\ y=3.32673x+86.32673 \end{gathered}[/tex]
ai) a = slope, b = y-intercept of the function
[tex]\begin{gathered} \text{from the model we got:} \\ m\text{ = }3.32673 \\ \text{slope = }3.32673 \\ b\text{ = y-intercept} \\ b\text{ = }86.32673 \end{gathered}[/tex]
[tex]\begin{gathered} aii)\text{ r = correlation coefficient} \\ r\text{ = }\frac{S_{xy}}{\sqrt[]{S_{x\times\text{ }\times}S_{yy}}} \\ \\ \text{From the model, r = }0.944502376 \end{gathered}[/tex]
b) when feet = 28 cm long, height = ?
x = 28, y = ?
[tex]\begin{gathered} \text{substitute for x in the model:} \\ y=3.32673x+86.32673 \\ y=3.32673(28)+86.32673 \\ y=\text{ }179.47517 \end{gathered}[/tex]
To the nearest tenth number, the height 179.5 cm
