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Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below.

HOURS OF TV AGE
1 45
3 30
4 22
3 25
6 15

a. Determine which variable is the dependent variable.
b. Compute the least squares estimated line.
c. Compute the coefficient of determination. How would you interpret this value?

User YPCrumble
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1 Answer

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Final answer:

The dependent variable is the age of a person, the least squares estimated line can be computed using the formulas for slope and y-intercept, and the coefficient of determination measures the strength of the relationship between the variables.

Step-by-step explanation:

In this scenario, the independent variable is the number of hours of television watched in a day and the dependent variable is the age of a person.

To compute the least squares estimated line, you need to find the equation of the line that best fits the data. The equation is in the form ŷ = a + bx, where ŷ is the predicted value, a is the y-intercept, b is the slope, x is the independent variable, and y is the dependent variable. To find the least squares estimated line, you need to use the formulae for calculating the slope and the y-intercept.

The coefficient of determination, also known as R-squared, measures the proportion of the variance in the dependent variable that can be explained by the independent variable. It represents the strength of the relationship between the variables. A value close to 1 indicates a strong relationship, while a value close to 0 indicates a weak relationship.

User Nick Steele
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