The accompanying data on y = normalized energy

ddaeeric 2021-01-13 Answered

The accompanying data on y = normalized energy \(\displaystyle{\left[{\left(\frac{{J}}{{m}^{{2}}}\right)}\right]}\) and x = intraocular pressure (mmHg) appeared in a scatterplot in the article “Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts” (Current Eye Research, 2012: 43-49), an estimated regression function was superimposed on the plot.
\(\begin{array}{|c|c|}\hline x & 2761 & 19764 & 25713 & 3980 & 12782 & 19008 & 19028 & 14397 & 9606 & 3905 & 25731 \\ \hline y & 1553 & 14999 & 32813 & 1667 & 8741 & 16526 & 26770 & 16526 & 9868 & 6640 & 1220 & 30730 \\ \hline \end{array}\)
Here is Minitab output from fitting the simple linear regression model. Does the model appear to specify a useful relationship between the two variables?
\(\begin{array}{|c|c|}\hline \text{Predictor Coef SE Coef T P Constant} & -5090 & 2257 & -2.26 & 0.048 \\ \hline \text{Pressure} & 1.2912 & 0.1347 & 9.59 & 0.000 \\ \hline \end{array}\)
\([S=3679.36, R-Sq = 90.2\%, R-Sq(adj)=89.2\% ]\).

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Expert Answer

Caren
Answered 2021-01-14 Author has 96 answers

Step 1
Given:
[n=12]
Let us assume:
[α=0.05]
Given in the output:
[b1=1.2912]
SEb1=0.1347
Determine the hypothesis:
H0:β1=0
H0:β1q0
Compute the value of the test statistic:
[t=b1β1SEb1=1.291200.13479.59]
The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table B containing the t-value in the row [df=n2=122=10:]
[P<2×0.0005=0.001]
If the P-value is less than or equal to the significance level, then the null
hypothesis is rejected:
[P<0.05RejectH0]
There is sufficient evidence to support the claim that the slope of the population regression line is not zero, which means that the model appears to specify a useful relationship between the two variables.
Result:
Yes.

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