In: Statistics and Probability
1.A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The dependent variable is ______.
b) number of production runs
c) number of defects
d) production run
e) percentage of defects
2) In the equation y = m x + b, which represents a straight lime, b
is the __________.
a) slope of the line
b) origin
c) y-intercept of the line
d) x-intercept of the line
3) Determine the Pearson product-moment correlation coefficient for
the following data.
x 1 11 9 6 5 3 2
y 10 4 4 5 7 7 9
Here The answer of all above Questions with detailed explanation is given below,
1) Dependent variable is Number Of defects.
Here the quality manager wants to predict the number of defects of product. Here the number of defects in depends upon the number of production Runs. Here that's why here quality manager should take number of defects as dependent variable.
2) c) Y- intercept of line.
In simple linear regression the mathematical model is y= mx + b which is straight line equation. In which m represent the slope of line and b represents the intercept. Intercept in regression equation us represents the value of y Variable at X=0.
3) The Correlation coefficient is below,
The Pearson products moment correlation coefficient is Also called as correlation coefficient in short .the given data is,
x 1 11 9 6 5 3 2
y 10 4 4 5 7 7 9
The calculation is given below,
X Values ∑ = 37
Mean = 5.286
∑(X - Mx)2 = SSx = 81.429
Y Values ∑ = 46
Mean = 6.571
∑(Y - My)2 = SSy = 33.714
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = -49.143
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -49.143 / √((81.429)(33.714)) = -0.9379
Meta Numerics (cross-check)
r = -0.9379
The value of R is -0.9379.
This is a strong negative correlation, which means that high X variable scores go with low Y variable scores.
The value of R2, the coefficient of determination, is 0.8797.
Hope you understood then RATE POSITIVE ?. In case of any queries please feel free to ask in comment box.
Thank you.