Acoach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a game. the table below shows the data: number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4 score in the game (y) 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 which best fits the data. (3 points) part c: what does the slope and y-intercept of the plot indicate? (3 points)

Part a.we can actually see that for every 0.5 increase in the value of x, there is a corresponding and constant increase of 3 in the value of y. so the answer to this is: yes and the correlation is linear.  part b.the general form of a linear function is: y = m x + bwhere m is the slope and b is the y –intercept  calculating for m using the formula: m = (y2 – y1) / (x2 – x1)m = (8 – 5) / (0.5 – 0)m = 3 / 0.5m = 6  the y-intercept b is the value of y when x = 0, therefore: b = 5  the complete equation of the function is: y = 6 x + 5  part c.the slope represents the rate of change, this means that there is an increase of 6 in the value of y for every increase of 1 in the value of x. 

A. when the score is plotted on a graph against hours spent practicing, the points all fall on a straight line. this means there is perfect correlation between hours and score. (the correlation coefficient is r=1.)b. the regression function of the calculator shows the function to be.. score = 6*hours +5or.. y = 6x +5c. the slope is the score added for each additional hour of practice (6 points). the y-intercept is the score with no hours of practice.

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