Define the relationship of interest and a data collection technique. I have some

Question

Define the relationship of interest and a data collection technique.

I have some information below. Is this a good project for correlation regression?

Determine the appropriate sample size and collect the data.

Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables. Describe the relationship in terms of strength and direction.

Construct a model of the relationship and evaluate the validity of that model.

Show all work to receive full credit. Provide complete sentence explanations for each of the above.

What are the two variables of interest? What linear relationship are you interested in exploring? Weight vs. Height

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

Is there a linear relation between infants' heights and their head girths Index Height(in.) Head Girths (in.) 1 27.75 17.1 2 24.5 17.1 3 25.5 17.1 4 26 17.3 5 25 16.9 6 27.75 17.6 7 26.5 17.3 8 27 17.5 9 26.75 17.3 10 26.75 17.5 11 27.5 17.5

Explanation / Answer

Here independent variable is height and dependent variable is head girths.

Now we have to test the hypothesis that,

H0 : Rho = 0 Vs H1 : Rho not= 0

where Rho is popualtion correlation between height and head girths.

Assume alpha = level of significance = 0.05

Here test statistic follows t-distribution with n-2 degrees of freedom.

The test statistic is,

t = r*sqrt(n-2) / sqrt(1-r^2)

where r is sample correlation between height and head girths.

n is number of data pairs.

Now we have to find p-value or critical value for taking decision.

P-value we can find in EXCEL.

syntax :

=TDIST(x, deg_freedom, tails)

where x is absolute value of test statistic.

deg_freedom = n-2

tails = 2

Decision rule :

If P-value < alpha then reject H0 at 5% level of significance otherwise accept H0.

We can test this hypothesis using MINITAB.

steps :

ENTER data into MINITAB sheet --> STat --> Basic Statistics --> COrrelation --> Variables : select height and head girths --> Click on display p-values --> ok

————— 6/18/2017 11:20:05 AM ————————————————————

Welcome to Minitab, press F1 for help.

Correlations: Height(in.), Head Girths (in.)

Pearson correlation of Height(in.) and Head Girths (in.) = 0.690
P-Value = 0.019

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is relationship between height and head girths.

Now we have to fit regression of head girths on height.

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : select head girths --> Predictors : select height --> Results :select second option --> ok --> ok

Regression Analysis: Head Girths (in.) versus Height(in.)

The regression equation is
Head Girths (in.) = 13.6 + 0.139 Height(in.)

Predictor Coef SE Coef T P
Constant 13.601 1.290 10.54 0.000
Height(in.) 0.13947 0.04874 2.86 0.019

S = 0.168693 R-Sq = 47.6% R-Sq(adj) = 41.8%

Analysis of Variance

Source DF SS MS F P
Regression 1 0.23298 0.23298 8.19 0.019
Residual Error 9 0.25611 0.02846
Total 10 0.48909

Here intercept = 13.6

Slope = 0.139

Interpretation of slope : For one unit change in height will be 0.139 unt increase in head girths.

Now we can test the hypothesis for overall significance and individual significance.

Overall significance :

Here we have to test the hypothesis that,

H0 : Bj=0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Here test statistic follows F-distribution.

Test statistic = 8.19

P-value = 0.019

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

Testing individual slope :

Here we can test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is popualtion slope for independent variable.

Here test statistic follows t-distribution.

Test statistic = 2.86

P-value = 0.019

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Height is significant variable or population slope for height is differ than 0.

Now R-sq = 47.6% = 0.476

It expresses the proportion of variation in head girths which is explained by variation in height.

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