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Created: Nov 12, 2017
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effects of smoke on infants part 2
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Data set 1. effect of smoke on infants   [Info]
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Result 1: Scatter Plot   [Info]
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This scatterplot is graphing the quantitative variables of weight and length.

No outliers should be removed. 

My p-value should be very close to 0.

My line of best fit will have a slope of 0.0024 and a standard deviation of 3.5. 

 

Result 2: Simple Linear Regression   [Info]
Simple linear regression results:
Dependent Variable: Length in cm
Independent Variable: Weight in Grams
Length in cm = 42.401967 + 0.0023777771 Weight in Grams
Sample size: 57
R (correlation coefficient) = 0.48952036
R-sq = 0.23963018
Estimate of error standard deviation: 3.5415865

Parameter estimates:
ParameterEstimateStd. Err.AlternativeDFT-StatP-value
Intercept42.4019671.9467454 ≠ 05521.780951<0.0001
Slope0.00237777710.00057112538 ≠ 0554.16331880.0001

Analysis of variance table for regression model:
SourceDFSSMSF-statP-value
Model1217.40776217.4077617.3332240.0001
Error55689.8559212.542835
Total56907.26369

My correlation coefficient is 0.48952036, therefore, there is a moderate positive relationship.

Yes, my terms are significant. 

My line of best fit has an intercept of 42.4 and a slope of 0.00237.

My R-sq is 0.2396 which expressed how well the regression line approximates the data points. 



 

Result 3: Simple Linear Regression line of best fit   [Info]
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No, it is not a good fit for my data because an R-sq of 1 would mean that the line perfectly represents the data and my R-sq is 0.23 which isn't even close to being perfect.

No, my data is not correlated.


 

Result 4: Simple Linear Regression QQ residuals   [Info]
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Yes, my expected values follow a normal distribution and appear to be left-skewed. 


 

Result 5: Simple Linear Regression predicted values vs   [Info]
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Yes, my residual plot implies that the linear model is a good fit.


No, the results were the same.


Yes, it is different than the model for my whole data set because there was less data that was more alike and therefore made the line of best fit almost perfect.


Result 6: Multiple Linear Regression 2   [Info]
Multiple linear regression results:
Dependent Variable: Weight in Grams
Independent Variable(s): Gestation Period (Weeks), Length in cm
Weight in Grams = -7532.7019 + 194.34399 Gestation Period (Weeks) + 68.951014 Length in cm

Parameter estimates:
ParameterEstimateStd. Err.AlternativeDFT-StatP-value
Intercept-7532.70191288.8147 ≠ 054-5.8446739<0.0001
Gestation Period (Weeks)194.3439930.159715 ≠ 0546.4438272<0.0001
Length in cm68.95101419.020375 ≠ 0543.62511330.0006

Analysis of variance table for multiple regression model:
SourceDFSSMSF-statP-value
Model2219243291096216535.813454<0.0001
Error5416528897306090.69
Total5638453226

Summary of fit:
Root MSE: 553.25463
R-squared: 0.5702
R-squared (adjusted): 0.5542

This data now represents all my quantitative data. It includes the gestation period which hasn't been included in this part of the project. This changed my R-sq.

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=73668">effects of smoke on infants part 2 </A>

Comments
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By xg15
Nov 18, 2017

The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true. Usually it is 0.05 or 0.01.
When determine whether a slope is significant or not, we compare the P-value with the significance level
R^2 is the percentage of variance of response explained by linear model

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