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# Statistics - Correlation Coefficient, Regression, Slope, Intercept, Mean, and Deviation

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1- The correlation coefficient is used to determine:
a. A specific value of the y-variable given a specific value of the x-variable
b. The strength of the relationship between two variables
c. A specific value of the x-variable given a specific value of the y-variable
d. None of these

2- Larger values of r2 imply that that the observations are more closely grouped around:

a. The sample mean for the y-variable
b. The sample mean for the x-variable
c. The least squares regression line
d. The y-intercept

3- In a regression analysis, if r2 = 1 then:

a. SSE = SST
b. SSE = 1
c. SSR = SSE
d. SSR = SST

4- A chemical engineer is investigating the effect of process operating temperature on product yield. The study results in the following data; use your knowledge of least squares regression to construct a linear model for predicting yield from temperature. These data apply throughout question 4.

Temp(Celsius) Yield (grams)
100 43.6215
110 46.6231
120 58.2752
130 58.8906
140 65.4354
150 74.5960
160 72.5202
170 79.0639
180 83.6280
190 84.4351

Calculate the slope and intercept of the least squares regression model by hand, which requires only the means and standard deviations of X and Y, and the correlation coefficient (here r = 0.9805).

4 a)The mean of Temperature is in the range:

a. 60-70
b. 70-80
c. 80-90
d. 90-100
e. 100-110
f. 110-120
g. 120-130
h. 130-140
i. 140-150
j. 150-160

4 b)- The mean of Yield is in the range:

a. 60-70
b. 70-80
c. 80-90
d. 90-100
e. 100-110
f. 110-120
g. 120-130
h. 130-140
i. 140-150
j. 150-160

4 c)- The standard deviation of Yield is in the range:

a. 0-5
b. 5-10
c. 10-15
d. 15-20
e. 20-25
f. 25-30

4 d) - The intercept of the fitted regression line is closest to:

a. 9.40
b. 2.03
c. 0.473
d. -1.87

4 e) - The slope of the fitted regression line is closest to:

a. 9.40
b. 2.03
c. 0.473
d. -1.87

4 f) - The yield predicted by the regression model for a temperature of 150 degrees is closest to:

a. 65.435
b. 74.596
c. 72.520
d. 69.074
e. 73.803

4 g) - The residual error for a temperature of 150 degrees is closest to:

a. +0.033
b. -5.522
c. +5.522
d. -0.107
e. +0.107

https://brainmass.com/statistics/regression-analysis/correlation-coefficient-regression-slope-intercept-mean-sd-515354

#### Solution Preview

I've included my explanation in the word document attached.

1- The correlation coefficient is used to determine:
a. A specific value of the y-variable given a specific value of the x-variable
b. The strength of the relationship between two variables
c. A specific value of the x-variable given a specific value of the y-variable
d. None of these

The correlation coe.fficient ranges from -1 to 1. When the value is close to -1 or 1, it indicates strong negative or positive correlation between the two variables. Therefore, b is the right choice.
2- Larger values of r2 imply that that the observations are more closely grouped around:

a. The sample mean for the y-variable
b. The sample mean for the x-variable
c. The least squares regression line
d. The y-intercept
as R^2 becomes larger and larger, all the observations are closer to the regression line. Therefore, c is the right answer.
3- In a regression analysis, if r2 = 1 then: