Suppose that we want to find a regression equation relating
systolic blood pressure (y) to weight
(x1), age (x2) and smoking
status (0 = does not smoke, 1 = smokes less than one pack per
day, 2 = smokes one or more packs per day). Use the Minitab
outputs below to test whether or not the smoking status variable
adds to the predictive value of a model which already contains
weight and age, using α = .05. i.e., test the hypothesis
H0 : β4 =
β5 = 0 vs H1 : at least
one of β4, β5 ≠ 0 in the
model y = β0 +
β1x1 +
β2x2 +
β3x3 +
β4x4 +
β5x5. ------------------------------------------ Regression Analysis: SYSTOLIC versus WEIGHT, AGE
Regression Analysis: SYSTOLIC versus WEIGHT, AGE, x4, x5
What is the value of the test statistic? (2 decimals) |
sample size n= | 78 | ||||
SSE for complete model :SSEc = | 5712.3 | ||||
SSE for reduced model :SSER = | 6193.9 | ||||
c =coefficients in complete model = | 4 | ||||
r =coefficient in reduced model = | 2 | ||||
Partial F=((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) = | 3.08 |
Suppose that we want to find a regression equation relating systolic blood pressure (y) to weight...
' - [2 marks] Suppose that we want to find a regression equation relating systolic blood pressure (v) to weight (x1), age (x2) and smoking status (0 = does not smoke, 1 = smokes less than one pack per day, 2 = smokes one or more packs per day). Use the Minitab outputs below to test whether or not the smoking status variable adds to the predictive value of a model which already contains weight and age, using a =...
Suppose that we want to find a regression equation relating systolic blood pressure (y) to weight (x1) and age (x2) and exercise status using the following data (note that only the first 4 rows of data are shown): ↓ C2 C5 C6 C8 Age Exercise Weight Systolic 1 36 1 215 163 2 43 1 127 132 3 47 0 132 138 4 48 2 196 148 Since exercise status is categorical, we first create the following three indicator variables,...
In this exercise use the Peruvian blood pressure data set, provided in the file peruvian.txt. This dataset consists of variables possibly relating to blood pressures of n = 39 Peruvians who have moved from rural high altitude areas to urban lower altitude areas. The variables in this dataset are: Age, Years, Weight, Height, Calf, Pulse, Systol and Diastol. Before reading the data intoMATLAB, it can be viewed in a text editor. This question involves the use of multiple linear regression...
Regression Analysis: Score2 versus Score1 The regression equation is Score2 = 1.12 + 0.218 Score1 Predictor Constant Score: Coef SE Coef T P 1.1177 0.1093 10.23 0.000 0.21767 0.01740 12.51 0.000 S = 0.127419 R-Sq = 95.7% R-Sq(adj) = 95.1% Analysis of Variance Source DF SS Regression 1 2.5419 Residual Error 7 0.1136 Total 8 2.6556 MS 2.5419 0.0162 F 156.56 P 0.000 At 1% significance, does the output indicate there a linear relationship between Score 1 and Score 2?...
The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 9.048 3.135 2.886 0.010 x1 0.284 0.111 2.559 0.000 x2 − 1.116 0.581 − 1.921 0.028 x3 − 0.194 0.189 − 1.026 0.114 x4 0.583 0.336 1.735 0.001 x5 − 0.025 0.026 − 0.962 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 1,895.93 379.2...
The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.987 2.967 2.690 0.010 x1 0.122 0.031 3.920 0.000 x2 − 1.120 0.053 − 2.270 0.028 x3 − 0.063 0.039 − 1.610 0.114 x4 0.523 0.142 3.690 0.001 x5 − 0.065 0.040 − 1.620 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 371000 742...
Regression Analysis: Rating versus Shelf position Method Categorical predictor coding (1, 0) Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 2 1511 755.6 5.50 0.013 Shelf position 2 1511 755.6 5.50 0.013 Error 20 2748 137.4 Total 22 4259 Model Summary S R-sq R-sq(adj) R-sq(pred) 11.7222 35.48% 29.03% 21.34% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 32.85 4.43 7.41 0.000 Shelf position bottom 7.40 7.35 1.01 0.326 1.30 top 18.15 5.58 3.26 0.004 1.30...
Data from n = 113 hospitals in the United States are used to assess factors related to the likelihood that a hospital patients acquires an infection while hospitalized. The variables here are y = infection risk, x1 = average length of patient stay, x2 = average patient age, x3 = measure of how many x-rays are given in the hospital. The Minitab output is as follows: Regression Analysis: InfctRsk versus Stay, Age, Xray Analysis of Variance Source DF Adj SS...
Suppose that you fitted the model E(y) = β0 + β1x + β2x2 to n = 20 data points and obtained the following MINITAB printout. Regression Analysis: y versus x, x-sq Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 2 41225.4 20612.7 987.09 0.000 Error 17 355.0 20.9 Total 19 41580.4 Model Summary S R-Sq R-Sq(adj) 4.56972 99.15% 99.05% Coefficients Term Coef SE Coef T-Value P-Value Constant 12.53 3.40 3.69 0.002 x 9.74 1.49 6.54 0.000...
6. (textbook) An analyst fitted a regression model to predict city MPG using as predictors Length (of car in inches), Width (of car in inches) and Weight (of car in pounds). a. Intuitively, what association do you expect between the explanatory variables and MPG? b. Do you see anything of concern about these variables being used as explanatory variables? Explain S c. What does the matrix plot done in class show you? Explain d. Write the null and alternative hypothesis...