Question

A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a game. The table shows
the data:
Number of hours spent practicing
0 0.5
1
1.5
2
2.5 3
3.5 4
Score in the game
5
8
11
14 17 20 23 26 29
Part A: Is there any correlation between the number of hours spent practicing and the score in the game? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Answer 1

Answer:

(A) There is a perfect correlation between the two variables.

(B) The line of best fit is, y = 6 x + 5.

(C) The slope of a regression line represents the average rate of change.

     Intercept is the point where the line crosses the x-axis.

Step-by-step explanation:

(A)

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

Compute the correlation coefficient between the number of hours spent practicing and the score in the game using the Excel function "CORREL(array1, array2)".

The correlation coefficient between the number of hours spent practicing and the score in the game is 1.00.

This implies that there is a perfect correlation between the two variables.

(B)

Compute the line of best fit as follows:

Consider the points (1.5, 14) and (3.5, 26):

$(y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})\\\\(y-14)=\frac{26-14}{3.5-1.5}\ (x-1.5)\\\\y-14=6x-9\\\\y=6x+5$

Thus, the line of best fit is, y = 6 x + 5.

(C)

The slope of a regression line represents the average rate of change in y caused by x.

The y-intercept is the value of y for x = 0, i.e. it is the point where the line crosses the x-axis.