Title Correlation And Simple Linear Regression A Study Was Conducted To Explore The Relationship Of Students Performan 1 (96.42 KiB) Viewed 44 times
Title: Correlation and Simple Linear Regression A study was conducted to explore the relationship of students' performance on a particular college mathematics achievement test (Y) to two factors. Factor 1 (X₁) is the teacher's rating (1-10, a higher rating means more effective) on the effectivity of strategies used in discussing the lesson related to the test. Factor 2 (X₂) on the other hand is the quality of mathematics background as reflected by the students' general weighted average in all mathematics courses undertaken in the senior high school. Here is the collected data. Teachers Rating (X) SHS GWA (X₂) 7 1 10 5 7 4 5 75 80 79 91 94 87 93 3 8 6 75 81 92 Score in the Achivement Test (1) 87 60 96 77 80 89 88 75 94 85 A. Compute the correlation coefficient between (1) Y and X₁ and (2) Y and X2 to identify which factor is related to students' performance. Complete the following before providing the coefficients. $x ——___ $x-_—___ _«x»£x_($x) SXX₁ = 11 SXX₂ = x₂ -8. n Σ SYY = -$($) 71 sxr = 2*wm- ($(2)_ xuy )( ) = 71 )( SX₂Y=x₂0;- ( ) VX₁Y SX.Y (SXX₂) (SYY) SX,Y (SXX₂) (SYY) VX₂Y Brief Interpretation: 71 )( )(
B. Estimate a linear regression line between Y and the factor more related to it (based from the results in A). After which, compute the coefficient of determination and interpret the result. Also, predict the performance of a student if teachers rating is 9 or his GWA is 83. Assume that the given data does violate any residual assumption. Mean of the independent variable: Mean of the dependent variable: 4-8 b₁ = ( )-( )( )=. The estimated regression line is This mean that R²=bSXY )( SYY This mean that Prediction: -(100%) = ( ) (100%) =
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