Problem # 4 (12 points) The following scatter plot illustrates the association b

Question

Problem # 4 (12 points) The following scatter plot illustrates the association between College Attainment (percent of 25+ year olds with a BA or higher degree) and Median Hourly Wage (in $) measured for the 50 States in 2013. (Available at:www.bls.ov/loes/currentlo 22.00 20.00 o-79.0.22 16.00 14.00 40 15 20 College Attainment, in % of 25+ year olds with BA or higher (2 poin a. What does each dot in this scatter plot represent? b. In this model, the explanatory variable is and the response variable is c. Circle a reasonable estimate for the value of the correlation coefficient r in this mod 1) 0.135 I1)-0.655 )1.35 IV) 0.702 Give reason/s) for your choice.

Explanation / Answer

a) Each dot in the scatter plot represents a coordinate at which value on x-axis give the corresponding value of output y

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b) In this model, the explanatory variable is x (college attainment) and response variable (median hourly wage) is y.

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c) The correlation coefficient should be in the range -1 to 1

-1 to 0... negative relationship; 0 to 1 positive relationship.

Hence among the options 0.702 is the apt answer

option D

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d) Given LSR,

y = 8.79 + 0.29 x

If the x increases by 5%, y increses by

For x = 100, y = 37.79

If x = 105, y = 8.79 + 0.29 (105) = 39.24

Hence, % change in y is 3.83%

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e) If x=23,

y = 8.79 + 0.29 (23) = 15.46

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