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A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. Based on this information, the Y intercept should be interpreted as: a. When a student's weekly income equals zero, the mean value of his/her weekly spending is estimated to be $20.90. b. When a student's weekly spending equals zero, the mean value of his/her weekly income is estimated to be $21.56. c. When a student's weekly income equals zero, the mean value of his/her weekly spending is estimated to be $21.56. d. When a student's weekly spending equals zero, the mean value of his/her weekly income is estimated to be $20.90.

Question

A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. Based on this information, the Y intercept should be interpreted as:

a.	

When a student's weekly income equals zero, the mean value of his/her weekly spending is estimated to be $20.90.

b.	

When a student's weekly spending equals zero, the mean value of his/her weekly income is estimated to be $21.56.

c.	

When a student's weekly income equals zero, the mean value of his/her weekly spending is estimated to be $21.56.

d.	

When a student's weekly spending equals zero, the mean value of his/her weekly income is estimated to be $20.90.

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Solution

The correct answer is:

a. When a student's weekly income equals zero, the mean value of his/her weekly spending is estimated to be $20.90.

The Y-intercept in a linear regression model represents the estimated value of the dependent variable (in this case, spending) when the independent variable (in this case, income) is zero. Therefore, if a student's weekly income is zero, we would predict their weekly spending to be $20.90, on average.

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