Question

10.2.21-T Question Help * 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 44 years. ls the result within 5 years of the actual Best Actor winner, whose age was 43 years? Best Actress 29 32 28 64 30 35 46 28 61 23 44 56 Best Actor 45 38 37 44 53 50 60 48 37 56 43 35 Find the equation of the regression line. Round the constant to one decimal place as needed. Round the coefficient to three decimal places as needed.)

Answer 1

	X	Y	X * Y	X2
	29	45	1305	841
	32	38	1216	1024
	28	37	1036	784
	64	44	2816	4096
	30	53	1590	900
	35	50	1750	1225
	46	60	2760	2116
	28	48	1344	784
	61	37	2257	3721
	23	56	1288	529
	44	43	1892	1936
	56	35	1960	3136
Total	476	546	21214	21092

$\hat{Y} = a + bX$

Where , a :- is the Y intercept

b :- is the slope of the equation

$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

$a =( \Sigma Y - ( b * \Sigma X) ) / n$

$\hat{Y} = 53.5 - 0.201 X$

To find the best predicted age of the actor given the age of the actress is 44 years

$\hat{Y} = 53.5 - 0.201 (44)$

$\hat{Y} =45$

Actor's age is 45 years.