Math  /  Data & Statistics

QuestionThe least-squares regression equation is y^=762.7x+13,048\hat{y}=762.7 x+13,048 where yy is the median income and xx is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7285 . Complete parts (a) through (d). (a) Predict the median income of a region in which 30%30 \% of adults 25 years and older have at least a bachelor's degree. \35929(Roundtothenearestdollarasneeded.)(b)Inaparticularregion,29.6percentofadults25yearsandolderhaveatleastabachelorsdegree.Themedianincomeinthisregionis 35929 (Round to the nearest dollar as needed.) (b) In a particular region, 29.6 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is \38,860 38,860. Is this income higher than what you would expect? Why?
This is higher than expected because the expected income is $35,624\$ 35,624 (Round to the nearest dollar as needed.) (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not round.) A. For 0%0 \% of adults having a bachelor's degree, the median income is predicted to be $\$ \square . B. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is \square %\%, on average. C. For a median income of $0\$ 0, the percent of adults with a bachelor's degree is \square \%. D. For every percent increase in adults having at least a bachelor's degree, the median income increases by $\$ \square , on average.

Studdy Solution
Interpret the slope of the regression equation, which is 762.7762.7.
Option D is correct: For every percent increase in adults having at least a bachelor's degree, the median income increases by $762.7\$762.7, on average.
The solutions are: (a) The predicted median income is $35,929\$35,929. (b) The actual income of $38,860\$38,860 is higher than the expected $35,625\$35,625. (c) The correct interpretation of the slope is option D: $762.7\$762.7.

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