I just need help answering these questions using the data that is provided. I ha
ID: 3242899 • Letter: I
Question
I just need help answering these questions using the data that is provided. I have the data below that I have already calculated I just need to use the data to answer the questions. Please Help!
Answer each question with complete sentences and include all relevant JMP files requested.
What are the two variables of interest? What linear relationship are you interested in exploring? Wight(Pounds) vs. Height(inches).
Which data collection technique will be used and why is it best?
What sample size is best for this data set and why?
Collect the data. Explain any issues you had during data collection. Include the JMP data file with your submission.
Is there a statistically significant relationship between the two variables? Describe the relationship in terms of strength and direction. Show your work by including the JMP output file.
Develop a linear model of this relationship. Include the JMP output file.
Is this a valid model to describe this relationship? Describe the fit of the model. Include the JMP output file.
Study for the linear relationship study for height and weight of people from a particular locality, who are selected by the process of simple random sampling without replacement. Index Height(Inches) Weight(Pounds) 1 64.57428 134.2647 2 68.68038 120.6936 3 67.53724 115.783 4 71.17732 128.6855 5 70.53514 134.7611 6 71.53411 118.3419 7 66.77301 106.1557 8 66.33636 126.3823 9 64.83095 114.3716 10 68.38247 130.2787 11 68.05038 123.3066 12 69.09149 122.8571 13 69.91046 125.6932 14 68.40737 111.7247 15 68.32559 125.5516 16 66.95555 119.9702 17 70.54816 132.6043 18 69.37805 132.6738 19 67.52012 117.4521 20 64.87142 101.8549 Fits and Diagnostics for Unusual Observations Regression Analysis: Weight(Pounds) versus Height(Inches) 21 69.13396 128.4418 Obs Weight(Pounds) Fit Resid Std Resid Regression Statistics 22 68.81192 134.0414 35 157.30 130.92 26.38 2.48 R Multiple R 0.402967026 23 67.56446 127.7511 48 150.28 122.05 28.23 2.66 R R Square 0.162382424 16.24% 24 68.16772 127.6172 74 105.39 129.66 -24.27 -2.28 R Adjusted R Square 0.153835306 15.38% 25 65.80687 139.3971 90 122.62 116.65 5.98 0.57 X Standard Error 10.73521727 26 64.92276 113.9381 R Large residual Observations 100 27 68.35584 147.5188 X Unusual X R-sq(pred)=12.62% 28 66.71546 132.6523 ANOVA 29 69.18196 132.8139 df SS MS F Significance F 30 65.88795 105.0942 Regression 1 2189.480045 2189.48 18.99850006 3.22918E-05 31 66.03733 127.5187 Residual 98 11293.99919 115.2449 32 69.44194 130.7305 Total 99 13483.47924 33 67.14847 128.5815 34 65.69442 122.5699 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% 35 69.42723 157.2961 Intercept -51.04927018 40.93837221 -1.24698 0.215377403 -132.2901375 30.19159712 -132.2901375 36 66.54503 121.1097 Height(Inches) 2.620963866 0.601314084 4.358727 3.22918E-05 1.427675636 3.814252096 1.427675636 37 69.04469 147.5061 Hypothesis 38 67.62036 117.493 H0: B1 = 0 ; H1 : B1 not= 0 39 69.59105 132.4472 T-stat for the slope of the regression equation: 4.3587 40 68.12343 118.1774 Critical Value: tcritical = 100-1,.025 = 1.984 41 71.22641 123.7319 Decision Rule: 42 66.43285 130.365 If test statistics value is greater than the critical value of t, then reject the null hypothesis, otherwise fail to reject the null hypothesis. 43 66.31808 122.8882 If P-value of the test statistics is less than the level of significance, then reject the null hypothesis. Otherwise, fail to reject the null hypothesis. 44 68.02724 107.8693 t = B1/SB1 = 2.621/.6013 = 4.3589 45 68.2876 118.591 The Test statistic is larger than the critical value 1.984, 4.3589 >1.984, so reject the null hypothesis. 46 66.91609 125.6467 B1 does not= 0 47 71.77546 148.6016 Regression Equation 48 66.04535 150.279 Weight(Pounds) = -51.0 + 2.621 Height(Inches) 49 69.01455 127.0678 From the above regression equation we can conclude that the variables height and weight are positively correlated to each other. 50 68.70744 128.7122 The two variables follow a positive trend. If height increases by one unit, then weight will increase by 2.621 units.Explanation / Answer
Please note that we can provide answers using open source tools. Also , please note that data collection and survey results are out of scope based on the question
What are the two variables of interest? What linear relationship are you interested in exploring?
The 2 variables of interest are Height and weight , we are interested in finding the effect of height on the weight as the fitted regression equation is
Weight(Pounds) = -51.0 + 2.621 Height(Inches)
Is there a statistically significant relationship between the two variables? Describe the relationship in terms of strength and direction. Show your work by including the JMP output file.
as the p value of the slope is 3.22918E-05, which is less than 0.05 , hence we can say that the relationship is signifcant.
Weight(Pounds) = -51.0 + 2.621 Height(Inches) , so there is a positive relationship between the 2 variables , with a increase of 1 unit of height , the weight increases by 2.621 units
Develop a linear model of this relationship. Include the JMP output file.
Weight(Pounds) = -51.0 + 2.621 Height(Inches)
is the linear regression model
Is this a valid model to describe this relationship? Describe the fit of the model. Include the JMP output file.
Yes , we see that the overall F signifcance value is 3.22918E-05, which is again less than 0.05 , hence the model is statistically signifcant.
H0 : The model is not significant
H1 : The model is signifcant
We reject the null hypothesis if p value is less than 0.05 .However the R2 value is
which means that model is able to explain only 16.23% variation of the data , hence the model is not doing a good job in capturing the variation
Height(Inches) 2.620963866 0.601314084 4.358727 3.22918E-05 1.427675636