A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table shows the data:

Number of hours spent studying

(x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score on science test

(y) 57 62 67 72 77 82 87 92 97

Part 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 that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

number of hoursstudentsspent studyingand thescoreon thescience testare inlinear correlation, afunctionthatbest fitsthedatais y = 4x + 60 and theslope and y-interceptof the plotindicatethaty -interceptis thelowest scorewithno time spent studying## Linear Correlation

Linear Correlationis ameasureof thedegreeto whichtwo variablesvary together, or ameasureof theintensityof theassociationbetweentwo variables.## What are the steps to solve this problem?

stepsare as follow:relationbetweenx and yvalues that forevery step changeof x = 0.5,every step changeof y = 2relationshipislinearpairs of pointsto get theslope and y-intercept(0, 60) and (1, 64)Calculatingtheslope:y – interceptis 60 as per point (0, 60)functionis y = 4x + 60slope and y-interceptof the plot indicatelowest scorewithno time spent studyingnumber of hoursstudentsspent studyingand thescoreon thescience testare inlinear correlation, afunctionthatbest fitsthedatais y = 4x + 60 and theslope and y-interceptof the plotindicatethaty -interceptis thelowest scorewithno time spent studyingLinear Correlationhere:Answer: From the table we see there is a relation between x and y valuesEvery step change of x = 0.5, every step change of y = 2This relation is linear. The formula for linear function is:y = mx + bUsing to pairs of points to get the slope and y-intercept(0, 60) and (1, 64)Calculating the slope:m = (64 – 60)/(1 – 0) = 4/1 = 4y – intercept is 60 as per point (0, 60)So the function isy = 4x + 60Part AYes. Described abovePart By = 4x + 60Part CSlope is the steepness of the line.y -intercept is the lowest score with no time spent studying