Answer:
a) y = -0.131x + 50.1
b) The predicted age of the best actor is within 5 years of the actual best actor's age
Explanation:
We were given a dataset. We will use this dataset to plot the graph as shown below:
We will plot the age of the best actor vs that of the best actress to obtain the graph below:
The equation of the straight line is given by:
[tex]\begin{gathered} \text{We will pick two coordinate points that lie along the straight line:} \\ (x_1,y_1)=(56,42.8) \\ (x_2,y_2)=(20,47.5) \\ slope,m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{47.5-42.8}{20-56} \\ m=\frac{4.7}{-36} \\ m=-0.1305 \\ \text{We will obtain the value for the y-intercept using the point-slope formula:} \\ y-y_1=m(x-x_1) \\ y-42.8=-0.1305(x-56) \\ y-42.8=-0.1305x+7.308 \\ \text{Add ''42.8'' to both sides, we have:} \\ y=-0.1305x+7.308+42.8 \\ y=-0.1305x+50.108 \\ y=-0.131x+50.1 \\ \\ \therefore y=-0.131x+50.1 \end{gathered}[/tex]
The equation is: y = -0.131x + 50.1
When the best actress age is 59, the predicted age of the best actor is obtained as shown below
[tex]\begin{gathered} y=-0.131x+50.1 \\ when\colon x=59 \\ y=-0.131(59)+50.1 \\ y=-7.729+50.1 \\ y=42.371\approx42 \\ y=42 \\ \\ \therefore y=42years \end{gathered}[/tex]
At 42 years, the predicted age is 4 years lesser than the actual best actor's age
Hence, the predicted age of the best actor is within 5 years of the actual best actor's age
