# Correlation coefficient, slope, y-intercept and SST

Please help me with the attached information on calculating the correlation coefficient, slope, y-intercept and SST using the given data.

© BrainMass Inc. brainmass.com October 25, 2018, 8:04 am ad1c9bdddfhttps://brainmass.com/statistics/correlation/correlation-coefficient-slope-y-intercept-sst-524351

#### Solution Summary

This solution is comprised of a detailed explanation for correlation coefficient. Correlation coefficient and regression equation is calculated manually by showing all the formulas and calculations. Full interpretation is given for correlation and regression analysis.

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

1- The correlation coefficient is used to determine:

Answer

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:

Answer

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:

Answer

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:

Answer

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:

Answer

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:

Answer

a. 9.40

b. 2.03

c. 0.473

d. -1.87

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

Answer

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:

Answer

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:

Answer

a. +0.033

b. -5.522

c. +5.522

d. -0.107

e. +0.107