Question

1. which expression represents \5 less than twice x\?

(1) ( 2 x - 5 )
(2) ( 5 - 2 x )
(3) ( 2 ( 5 - x ) )
(4) ( 2 ( x - 5 ) )

1. a survey of 100 students was taken. it was found that 60 students watched sports, and 34 of these students did not like pop music. of the students who did not watch sports, 70% liked pop music. complete the two - way frequency table.
2. suzanna collected information about a group of ponies and horses. she made a table showing the height, measured in hands (hh), and the weight, measured in pounds (lbs), of each pony and horse.

write the linear regression equation for this set of data. round all values to the nearest hundredth.
state the correlation coefficient for the linear regression. round your answer to the nearest hundredth.
explain what the correlation coefficient indicates about the linear fit of the data in the context of the problem.

Explanation:

Step1: Calculate the linear regression equation

Using a statistical software or calculator (such as TI - 84 Plus), input the data points \((x,y)\) where \(x\) is the height (in hands) and \(y\) is the weight (in pounds).
The linear regression equation is of the form \(y = ax + b\). After calculation, \(a\approx194.91\) and \(b\approx - 1879.27\). So the equation is \(y = 194.91x-1879.27\)

Step2: Calculate the correlation coefficient

Using the same statistical software or calculator, the correlation coefficient \(r\) is calculated. After calculation, \(r\approx0.99\)

Step3: Explain the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. The value of \(r\) ranges from \(- 1\) to \(1\). A value of \(r = 1\) indicates a perfect positive linear relationship, \(r=-1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship.
Since \(r\approx0.99\) (close to \(1\)), it indicates a very strong positive linear relationship between the height (in hands) of ponies and horses and their weight (in pounds). As the height increases, the weight also tends to increase in a nearly linear fashion.

Answer:

The linear regression equation is \(y = 194.91x - 1879.27\). The correlation coefficient is \(r\approx0.99\). The correlation coefficient of approximately \(0.99\) indicates a very strong positive linear relationship between the height and weight of ponies and horses.