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Created: Oct 17, 2018
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Blanco, Nereida, Lab 6

Research question: Does homework average have an existing correlation with the quiz average of students?

Explanatory variable: Homework Average

Response variable: Quiz Average

Least-squares line equation: ^y= 0.23123266x + 68.118953

Correlation coefficient (r): 0.55951575

Coefficient of determination (R^2): 0.31305788

After interpreting residuals plot and box plot, I can say that the linear model in this case is moderately appropriatebased on its coefficients and the fact that the residual plot has no pattern but is instead consistent with the plots being scattered across. As for the outliers, there are two outliers on both ends of the data which do have effect on the overal linear correlation but did not affect it enugh like to make it non- linear since it does have moderate relation after all.

My interpretation of the R^2 value is that it is accurate as to the data and results from both variables being correlated. Given that R^2 was 0.3 (rounded), it shows itis far from being perfect linear since it is not close to the value of 1 and for it applying to the least-squares regression line, it can apply but males it more of a moderate rather than a stron or perfect relation.

Result 1: Least-squares Simple Linear Regression   [Info]
Simple linear regression results:
Dependent Variable: Quiz Average
Independent Variable: HW Average
Quiz Average = 68.118953 + 0.23123266 HW Average
Sample size: 34
R (correlation coefficient) = 0.55951575
R-sq = 0.31305788
Estimate of error standard deviation: 6.5269069

Parameter estimates:
ParameterEstimateStd. Err.AlternativeDFT-StatP-value
Intercept68.1189534.6945415 ≠ 03214.510246<0.0001
Slope0.231232660.060551087 ≠ 0323.81880280.0006

Analysis of variance table for regression model:
SourceDFSSMSF-statP-value
Model1621.25415621.2541514.5832550.0006
Error321363.216442.600514
Total331984.4706

Residuals stored in new column: Residuals

Result 2: Least-squares Simple Linear Regression   [Info]

Result 3: Least-squares simple Linear Regression   [Info]

Result 4: Boxplot of Residuals   [Info]