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Correlation Mini Project

Correlation Mini Project. Michelle Han Period 1. Hours of sleep VS. First period grades. Hours of sleep. First period grades. Hours of sleep. First period grades. Is there a correlation between the hours of sleep a student gets on average and their first period percentage grades?

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Correlation Mini Project

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  1. Correlation Mini Project Michelle Han Period 1

  2. Hours of sleep VS. First period grades Hours of sleep First period grades Hours of sleep First period grades • Is there a correlation between the hours of sleep a student gets on average and their first period percentage grades? • A sample size of 30 students were asked.

  3. LSRL (Least Square Regression Line) • Also known as Line of best fit Linear Model Linear Equation Regression Equation y= first period percentage x= hours of sleep First period percentage= (.39462) + (.06349)(hours of sleep) Linear Regression y = a + bx a= .3946232135 b= .0634863577 r2= .7512241435 r= .8667318752

  4. R and R-Squared in Context • R is the correlation coefficient • Measures the scatter around the line • Strength of association between x & y • When r is .7 or better, it’s strong • When r is .4-.6, it’s moderate • When r is .3 and below, it’s weak R R- Squared There is a strong, positive linear association between hours of sleep and first period grades. 86.7% of the variation in the first period grades can be explained by the approximate linear relationship with hours of sleep.

  5. Predictions • Make a prediction for some who slept 10 hours using the model. • First period grade = .39462 + .06349 (10 hours) First period grade= .39462 + .6349 First period grade= 100.02 Our model predicts a first period grade of 100.02% if a student slept for 10 hours.

  6. Y-Intercept and Slope • Y-Intercept (a): Always plug in 0 as x. • Slope (b): Y-units Slope: For every hour of sleep, our model predicts an average increase of .06349 in the first period grade. Y-Intercept: If you sleep 0 hours, our model predicts a first period grade of .39462

  7. Residual Plot The points are residuals. The line is a prediction. No pattern/residuals are randomly scattered = a good fit Because the points or residuals are randomly scattered throughout the plot, our modes is a good fit.

  8. Scatter Plot

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