Data from “Applied Statistics and Probability for Engineers", Fourth Edition, by Douglas C. Montgomery & George C. Runger. The Excel multiple regression output below is for predicting pull strength from wire length and die height.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![Use the information below to answer the PULL STRENGTH questions that
follow.
Data from "Applied Statistics and Probability for Engineers", Fourth Edition, by
Douglas C. Montgomery & George C. Runger.
The Excel multiple regression output below is for predicting pull strength
from wire length and die height.
MULTIPLE REGRESSION EXCEL OUTPUT (PULL STRENGTH)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.990523843
R Square
0.981137483
Adjusted R Square 0.979422709
Standard Error
2.288046833
Observations
25
ANOVA
df
S
MS
Significance F
Regression
5990.771221
2995.385611 572.1671503
1.07546E-19
Residual
22
115.1734828 5.235158308
Total
24
6105.944704
Coefficients Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
2.263791434 1.060066238 2.135518851
0.04409945
0.065348623
4.462234246
Wire Length
2.744269643 0.093523844 29.34299438
3.90691E-19
2.550313062
2.938226225
Die Height
0.012527811 0.002798419 4.476746229 0.000188266
0.006724246 0.018331377](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F168d0f8b-cda6-411c-8512-e8f2d3c209f7%2Fb14d862c-60cb-4b9e-92f7-38a44dd25e65%2Fdil7gf9_processed.png&w=3840&q=75)
![PULL STRENGTH
Which of the following is a correct interpretation of the confidence interval
for the wire length coefficient?
The average pull strength is expected to go up by one unit when wire length is
between 2.550 and 2.939 units and die height is equal to one unit.
The average pull strength is expected to go up by between 2.550 and 2.939 units
when wire length increases by one unit and die height is kept constant.
The average pull strength is expected to go up by one unit when wire length
increases by between 2.550 and 2.939 units and die height is kept constant.
The average pull strength is expected to go up by one unit when wire length
increases by between 2.550 and 2.939 units and die height is equal to zero units.
The average pull strength is expected to go up by between 2.550 and 2.939 units
when wire length increases by one unit and die height is equal to zero units.
The average pull strength is expected to go up by between 2.550 and 2.939 units
when wire length is zero units and die height is
to one unit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F168d0f8b-cda6-411c-8512-e8f2d3c209f7%2Fb14d862c-60cb-4b9e-92f7-38a44dd25e65%2Fl2jbuw_processed.png&w=3840&q=75)
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