Question

3. 1/8 points | Previous Answers DevoreStat9 12.E.014 My Notes Ask Your Teacher The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y). Temp. 173 175 176 177 177 178 179 180 Ratio 0.74 1.25 1.50 0.93 1.05 1.12 1.14 1.70 Temp. 183 183 183 183 183 184 184 185 Ratio 1.5 1.58 1.57 2.15 2.11 0.88 1.43 0.90 Temp. Ratio 1.73 1.94 2.58 1.55 2.60 2.96 1.87 3.06 185 185 185 187 187 188 189 191 (a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.) (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 185. (Round your answer to four decimal places.) (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 185. (Round your answers to four decimal places.) (185, 0.90) (185, 1.73) (185, 1.94) (185, 2.58)

Answer 1

Solution-

(A) After running regression analysis in the excel, we get the following regression output as follows-

SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Square 0.693342164 0.480723356 0.457119873 79641509 Standard Error 0.4 Observations 24 ANOVA Significance F MS Regression Residual Total 4.6854643354.685464 20.36663 0.000172339 5.061231498 0.230056 9.746695833 23 Coefficients Standard Error tstat P-value Lower 95% Uper 95% -15.9359871 3.90032891 -4.08581 0.000489 -24.02477419-7.847200021 0.096418651 0.0213649314.51294 0.000172 0.052110496 0.140726806 Intercept X Variable 1

Regression equation is-

Y = -15.93599 + 0.09642 * X

(B) When X =185

then estimate of Y = -15.936 + 0.0964 * 185

= 1.9015

(C) Residuals is given by-

Estimate - Actual where estimate = 1.9015

Then residuals are given as-

1.0015

0.1715

-0.0385

-0.6785

TY!