Based on a regression analysis, a researcher concluded that 45% of the variance in minutes of activity per day can be explained by age, hours of sleep, and minutes spent on social media. What does the value 45% represent

Coefficient of determination, R²

Step-by-step explanation:

The proportion of variation of the dependent variable that can be explained by the regression line is defined by the coefficient of determination, R².

In the scenario described above, the proportion of variation in the number of minutes of activity per day(dependent variable) that can be explained by age, hours of sleep and minutes spent on social media (independent variables) which forms the regression line is 0.45 (45%) is the coefficient of determination while (1 - 0.45) = 0.55 is due to other factors.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.