Educators conducted a study of association between two variables. The explanatory (control) variable X represents hours...

Transcribed Image Text:

Educators conducted a study of association between two variables. The explanatory (control) variable X represents hours per week students devote to extra-curriculum activities. The response = Y is a final exam score measured in a 100-point scale. Summaries based on paired observations (X,Y) are Sample Mean X=4.5 hours and Sample SD = S[X] = 10 hours, Sample Mean Y = 78.3 points and Sample SD S[Y] =25 points = In addition, the sample covariance was found as S(X,Y)=-160 1. Find the correlation between X and Y 2. Determine the coefficients for a linear model that will be used to predict student's test score, in the form ý bothị X where by denotes slope of the model and by is its intercept. 3. Jane's activities were: X 5 hours and her score was Y = 76. Evaluate her projected final score and find whether the observation (X-5, Y=76) would be above or below the fitted line. 4. Peter's activity time was X= 4 hours and his final exam score was Y = 80. Evaluate his projected score and find whether the observation (X= 4, Y=80) would be above or below the fitted line. Educators conducted a study of association between two variables. The explanatory (control) variable X represents hours per week students devote to extra-curriculum activities. The response = Y is a final exam score measured in a 100-point scale. Summaries based on paired observations (X,Y) are Sample Mean X=4.5 hours and Sample SD = S[X] = 10 hours, Sample Mean Y = 78.3 points and Sample SD S[Y] =25 points = In addition, the sample covariance was found as S(X,Y)=-160 1. Find the correlation between X and Y 2. Determine the coefficients for a linear model that will be used to predict student's test score, in the form ý bothị X where by denotes slope of the model and by is its intercept. 3. Jane's activities were: X 5 hours and her score was Y = 76. Evaluate her projected final score and find whether the observation (X-5, Y=76) would be above or below the fitted line. 4. Peter's activity time was X= 4 hours and his final exam score was Y = 80. Evaluate his projected score and find whether the observation (X= 4, Y=80) would be above or below the fitted line.