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Do four regression analyses using the Anscombe Quartet (1973) Data Analysis Tool in Excel Any Statistical package Summarize t

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Do four regression analyses using the Anscombe Quartet (1973) Data Analysis Tool in Excel Any Statistical package Summarize t

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R RGui (64-bit) File History Resize Windows R R Graphics: Device 2 (ACTIVE) tled-R Editor R xl-c (10, 8, 13, 9, ll, 14, 6, 4,

Then run the linear regression.

regl Call: lm (formula yl xl) Residuals: Min 10 Median 3Q Max -1.92127-0.45577 -0.04136 0.70941 1.83882 Coefficients: Estimat

> reg2 Call: lm (formula y2 x2) Residuals: Min Median 30 Max -1.9009 -0.7609 0.1291 0.9491 1.2691 Coefficients Estimate Std.

> reg3 Call: lm (formula = v3 x3) Residuals: Min Median 3Q Max -1.1586 -0.6146 -0.2303 0.1540 3.2411 Coefficients: Estimate S

reg4 Call: = v4 x4) lm (formula Residuals: 30 Min 10 Median Max 0.000 1.839 -1.751 -0.831 0.809 Coefficients: Estimate Std. E

For all the 4 cases we see that the Multiple R-squared values are 0.66 and around it. This is because of the presence of outlier in the data set which can be clearly seen from the scatter plots.

So, now we remove the outlier and re-run the regression.

Data Set 2

RRGui (64-bit) File Edit Packages Windows Help RRGraphics Device 2 (ACTIVE) R Untitled R Editor v4-c (6.58,5.76,7.71, 8.84,8.Now, the multiple R-squared value is 1. So there is a perfect relationship exists between x2and y2.

R RGui (64-bit) X File Edit Packages Windows Help RRGraphics Device 2 (ACTIVE R Untitled R Editor y2=c (9.14,8.14,8.74,8.77,9So, we have seen that after removing the outlier the multiple R-squared become 1 indicating a perfect linear relationship exhibited.

Data Set 4

R RGui (64-bit) File Edit Packages Windows Help aphics: Device 2 (ACTIVE R Untitled REditor RR Console par (mfrow=c ( 2, 2 ))

Here, after removing the outlier we can see that there exists a singularity in x values so that no regression can be fitted and hence no multiple R-squared values can be found but as the standard deviation of x becomes zero.

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