Difference between revisions of "JAR v.IS Project Findings"
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* Errors/Residuals are normally distributed and have a population mean of zero | * Errors/Residuals are normally distributed and have a population mean of zero | ||
</p> | </p> | ||
+ | {| style="width:100%; vertical-align:top; margin-top:5px;" | ||
+ | |- | ||
+ | | style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=3 face="Century Gothic">Assumption 1: Linearity</font></div><br/> | ||
+ | |||
+ | [[File:Assumption_1n3.png|700px|center]] | ||
+ | {|style="width:100%;vertical-align:top;margin-top:20px;" | ||
+ | |- | ||
+ | |style="vertical-align:top;width:30%;" | <div style="background: #ffffff; text-align:center; line-height: wrap_content; text-align: center;font-size:12px">Residual by predicted plot</div> | ||
+ | |||
+ | <p>The points are quite symmetrically distributed around the line, and this indicates that the points are random and hence fulfills the linearity assumption.</p> | ||
+ | |||
+ | {| style="width:100%; vertical-align:top; margin-top:5px;" | ||
+ | |- | ||
+ | | style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=3 face="Century Gothic">Assumption 2: Zero expected mean error</font></div><br/> | ||
+ | |||
+ | [[File:Assumption_2.png|700px|center]] | ||
+ | {|style="width:100%;vertical-align:top;margin-top:20px;" | ||
+ | |- | ||
+ | |style="vertical-align:top;width:30%;" | <div style="background: #ffffff; text-align:center; line-height: wrap_content; text-align: center;font-size:12px">Distribution of residuals</div> | ||
+ | |||
+ | <p>The residuals largely follow a normal distribution with a mean close to zero and a standard deviation close to one.</p> | ||
+ | |||
+ | {| style="width:100%; vertical-align:top; margin-top:5px;" | ||
+ | |- | ||
+ | | style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=3 face="Century Gothic">Assumption 3: Homoscedasticity</font></div><br/> | ||
+ | [[File:Assumption_1n3.png|700px|center]] | ||
+ | {|style="width:100%;vertical-align:top;margin-top:20px;" | ||
+ | |- | ||
+ | |style="vertical-align:top;width:30%;" | <div style="background: #ffffff; text-align:center; line-height: wrap_content; text-align: center;font-size:12px">Residual by predicted plot</div> | ||
+ | |||
+ | <p>The distribution of the points in the plot is rather symmetrical, with no signs of increasing residuals with the increase of the predicted values (it is not funnel shaped). This indicates that the residuals have constant variance and are hence homoscedastic</p> | ||
+ | |||
+ | {| style="width:100%; vertical-align:top; margin-top:5px;" | ||
+ | |- | ||
+ | | style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=3 face="Century Gothic">Assumption 4: Independent Residuals</font></div><br/> | ||
+ | [[File:Assumption_4a.png|700px|center]] | ||
+ | {|style="width:100%;vertical-align:top;margin-top:20px;" | ||
+ | |- | ||
+ | |style="vertical-align:top;width:30%;" | <div style="background: #ffffff; text-align:center; line-height: wrap_content; text-align: center;font-size:12px">Residual by row plot</div> | ||
+ | |||
+ | <p>The scatter plot shows that the residuals are randomly distributed around the line and hence shows that they are time independent. This also suggests that residuals are not autocorrelated. | ||
+ | </p> | ||
+ | |||
+ | [[File:Assumption_4b.png|400px|center]] | ||
+ | {|style="width:100%;vertical-align:top;margin-top:20px;" | ||
+ | |- | ||
+ | |style="vertical-align:top;width:30%;" | <div style="background: #ffffff; text-align:center; line-height: wrap_content; text-align: center;font-size:12px">Durbin-Watson test of no autocorrelation</div> | ||
+ | |||
+ | <p>The Durbin-Watson d = 2.15, which is between the two critical values of 1.5 < d < 2.5. Therefore, we can assume that there is no first order linear auto-correlation in our multiple linear regression data</p> | ||
+ | |||
+ | {| style="width:100%; vertical-align:top; margin-top:5px;" | ||
+ | |- | ||
+ | | style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=3 face="Century Gothic">Assumption 5: Residuals are normally distributed</font></div><br/> | ||
+ | |||
+ | [[File:Assumption_5.png|700px|center]] | ||
+ | {|style="width:100%;vertical-align:top;margin-top:20px;" | ||
+ | |- | ||
+ | |style="vertical-align:top;width:30%;" | <div style="background: #ffffff; text-align:center; line-height: wrap_content; text-align: center;font-size:12px">Studentized Residual distribution</div> | ||
+ | |||
+ | <p>The residuals largely follow a normal distribution with a mean close to zero and a standard deviation close to one, hence fulfilling this assumption.</p> | ||
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|- | |- | ||
| style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=5 face="Century Gothic">Interpretation and Managerial insights</font></div><br/> | | style="vertical-align:top;width:20%;" | <div style="none: solid; border-width:2px; background: #FFFFFF; padding: 10px; font-weight:bold; text-align:center; line-height: wrap_content; text-indent: 20px; font-size:18px"><font color="#b1260e" size=5 face="Century Gothic">Interpretation and Managerial insights</font></div><br/> | ||
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+ | |||
+ | <p>A multiple stepwise linear regression was run to explain Ln(Total Engagement) for article performance from post message sentiment score, number of links, SQRT(Number of images) and article authors. These variables statistically significantly explained Ln(Total Engagement), F(33.79, 1.06) = 31.96, p < 0.0001***, adjusted R2 = 0.17. All selected variables provided statistically significantly to the explanation, p < .05. The article regression model has met all 5 assumptions highlighted above, and we believe that our sponsor can benefit from the knowledge of the different determinants of their different social media engagement performance based on the regression equation on their article performance.</p> | ||
+ | <br><br> | ||
+ | |||
+ | <p> | ||
+ | While our article explanatory regression models can explain up to 17-18% of the variation in the post’s engagement performance, insights can still be gleaned from it. Below are the points that can be drawn for the article regression model: | ||
+ | <br><br> | ||
+ | * A positive sounding post message to accompany the article can help increase engagement. | ||
+ | * Articles that contain too many embedded links may not perform well in terms of engagement. This could suggest possibly that viewer tend not to read the article or are referred elsewhere as a result. | ||
+ | * The number of images used in an article matters and more images can help improve the engagement level of the article. This is applicable for categories that require visually appealing information | ||
+ | * Authors A, B, C, D, E, F, G, H, I, and J are performing well and can be considered suited for writing their relevant categories whereas authors K, L, M, N, O, P, Q, R, S, and T are performing poorly, suggesting the need for either improvement or adjustment of assignments. | ||
+ | |||
+ | </p> |
Latest revision as of 22:02, 23 April 2017
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Multiple Linear Regression Model What makes a good Facebook post? This section outlines the explanatory model on the article dataset from Facebook Insights supplemented with our crawled variables to form a holistic complete article dataset.
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