In the United States, the high school dropout rate in 1980 was 14.1%. By 2005 th

Question

In the United States, the high school dropout rate in 1980 was 14.1%. By 2005 the dropout rate was 9.4%. a. Multiple choice: The linear regression model most closely fitting this data (where r represents high school dropout rate in percent and t represents years since 1980) is:

A. r=0.188t+14.1 C. r= –5.3t+14.1 B. r=5.3t+14.1 D. r= –0.188t+14.1

b. Use the model to predict high school dropout rate in 2019 (give answer to nearest tenth of a percent)

c. Fill in the blanks to interpret the slope of the equation: The rate of change of US high school dropout rate in percent with respect to time is ____________________ per ______________. (Include units of measurement.)

Explanation / Answer

Taking the year 1980 as the reference year that is 1980 will be the start point

=> t = 0 and r = 14.1

by 2005 the rate was = 9.4%

=> t = 2005 - 1980 = 25 and r = 9.4%

so we have got to points on the linear regression line (0,14.1) and (25,9.4)

so we could use these to form the model using the form

r = m*t + b

here m = slope = (9.4 - 14.1)/(25 - 0) = -0.188

plug any to the two points in the equation r = m*t + b and find b

=> r = 14.1 and t = 0

=> 14.1 = 0 + b , => b = 14.1

hence the linear regression model most closely fitting this data would be

r = - 0.188t + 14.1

option D is correct

b In the year 2019 , t = 2019- 1880 = 39

=> r = -.188*39 + 14.1 = 6.768

hence the dropout rate would be = 6.768 % = 6.8 %

c>

The rate of change of US high school dropout rate in percent with respect to time is = -.188 per year

the negative sign indicates that the rate is decreasing . that is the dropout rate is going down every year

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