Question

Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed actress/actor ages in various years,find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 59 years. Is the result within5 years of the actual Best Actor winner, whose age was 46 years?

Answer 1

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

Step-by-step 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:

`\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=(y_2-y_1)/(x_2-x_1) \\ m=(47.5-42.8)/(20-56) \\ m=(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}`

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

`\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}`

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