Question

4.(06.07 HC)A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table below shows the data:Number of hours spent studying 0 0.5 1(x)1.5 2 2.5 33.54Score on science test(y)57 62 67727782 879297Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)Part B: Write a function which best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)(10 points)

Answer 1

For part A. One way to know if there is a correlation between the data is to graph the data set, like this

Then, as can you see the data presents a positive linear correlation.

For part B. You can take the coordinates of two points and find the slope of the line using the formula

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}`

If you take

`\begin{gathered} (x_1,y_1)=(1,67) \\ (x_2,y_2)=(3,87) \\ \text{ You have} \\ m=(87-67)/(3-1) \\ m=(20)/(2) \\ m=10 \end{gathered}`

Now, using the slope formula, you can find the equation of the line in its slope-intercept form

`\begin{gathered} y-y_1=m(x-x_1) \\ y-67=10(x-1) \\ y-67=10x-10 \\ \text{ Add 67 on both sides of the equation} \\ y-67+67=10x-10+67 \\ y=10x+57 \end{gathered}`

Therefore, the function that best fits the data is

`y=10x+57`

For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.

The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.