4.2.13 Question He The least-squares regression equation is y-649.6x+15,421 wher

Question

4.2.13 Question He The least-squares regression equation is y-649.6x+15,421 where y is the median income and x 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 0.7541. Complete parts (a) through (d) 15 20 25 30 35 40 45 50 55 60 Bachelor's % (a) Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree. 34,909 (Round to the nearest dollar as needed.) (b) In a particular region, 28.3 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,186. Is this i higher than what you would expect? Why? This is Round to the nearest dollar as needed.) Vthan expected because the expected income is $

Explanation / Answer

Here the linear regression line is

y^ = 649.6 x + 15421

(a) Here x = 30%

so,

y^ = 649.6 * 30 + 15421 = $ 34,909

(b) Here for x = 28.5%

y^ = 649.6 * 28.5 + 15421 = $ 33,934.6 or $ 33,935

here this is more than expected because the expected income is $ 33,935

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