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 58 years. Is the result within 5 years of the actual Best Actor​ winner, whose age was 44 ​years?

Best Actress 27 31 30 64 34 32 46 29 61 22 43 53

Best Actor 41 38 36 46 48 47 57 53 39 53 44 35

1. Find the equation of the regression line.

y = _______ + (_________)x ​(Round the constant to one decimal place as needed. Round the coefficient to three decimal places as​ needed.)

2. The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 58 years is ________ years old. ​(Round to the nearest whole number as​ needed.)

3. Is the result within 5 years of the actual Best Actor​ winner, whose age was 44 ​years?

_(yes or no)________ the predicted age is__________________ the actual​ winner's age.

Answer 1

Find X⋅Y and X² as it was done in the table below.

X	Y	X⋅Y	X⋅X
27	41	1107	729
31	38	1178	961
30	36	1080	900
64	46	2944	4096
34	48	1632	1156
32	47	1504	1024
46	57	2622	2116
29	53	1537	841
61	39	2379	3721
22	53	1166	484
43	44	1892	1849
53	35	1855	2809

Find the sum of every column: :Use the following equations to find a and b 2089648.942 ΣΥΣΧ2 _ Σχ.ΣΧΥ-537 . 20686-472 . 20896 nx2 -(x) 12.20686 4722 n.ΣΧΥ-Σχ.ΣΥ 12-20896-472 . 537 n.ΣΧ2-(ΣΧ)2 12.20686 _ (472)2 2.5370.107 Substitute a and b in regression equation formula y = 48.942-0.107-z

( 2 )

y = 48.9 - 0.107 x

Given x = 58

then

y = 48.9 - 0.107 ( 58 )

= 42.694

= 43

The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 58 years is 43  years old

( 3 )

yes the predicted age is more than five years less than the actual​ winner's age.