A recent study1 examined several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Percentile, which gives percentile on a cognitive reaction test. The regression line for predicting Percentile from Years is:

Complete question:

A recent study examined several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Percentile, which gives percentile on a cognitive reaction test. The regression line for predicting Percentile from Years is:

Percentile 102 - 3.34 Years.

(a) Predict the cognitive percentile for someone who has played football for 7 years and for someone who has played football for 16 years. Enter the exact answers. The cognitive percentile for someone who has played football for 7 years is The cognitive percentile for someone who has played football for 16 years is

i) Cognitive percentile for someone who has played football for 7 years is 76.62

ii) Cognitive percentile for someone who has played football for 7 years is 46.56

Step-by-step explanation:

Given the regression equation: 102 - 3.34 (years)

Required:

Predict the cognitive percentile for someone who has played football for 7 years and for someone who has played football for 16 years

a) Cognitive percentile for someone who has played football for 7 years:

102 - 3.34 (years)

= 102 - 3.34(Y)

Substitute 7 for Y

102 - 3.34(7)

= 102 - 23.38

= 76.62

Cognitive percentile for someone who has played football for 7 years is 76.62

b) Cognitive percentile for someone who has played football for 16 years:

102 - 3.34 (years)

= 102 - 3.34(Y)

Substitute 7 for Y

102 - 3.34(16)

= 102 - 53.44

= 46.56

Cognitive percentile for someone who has played football for 7 years is 46.56

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)