9.) You work for a parts manufacturing company and are tasked with exploring the
ID: 3367865 • Letter: 9
Question
9.) You work for a parts manufacturing company and are tasked with exploring the wear lifetime of a certain bearing. You gather data on oil viscosity used and load. You see the regression output given below. What is the multiple regression equation?
b.) (lifetime) = 0.531*(viscosity) + 0.049*(load) + 164.556
c.) (lifetime) = 6.116*(viscosity) + 0.019*(load)
d.) (lifetime) = 6.116*(viscosity) + 0.019*(load) + 164.556
e.) (lifetime) = 6.116*(load) + 0.019*(viscosity) + 164.556
10.) Suppose the sales (1000s of $) of a fast food restaurant are a linear function of the number of competing outlets within a 5 mile radius and the population (1000s of people) within a 1 mile radius. The regression equation quantifying this relation is (sales) = 1.798*(competitors) + 5.674*(population) + 5.786. What would you expect the sales (in 1000s of $) to be of a store that has 2 competitors and a population of 15 thousand people within a 1 mile radius?
a.) 88.706
b.) 44.104
c.) 94. 492
d.) 82.92
e.) We do not know the observations in the data set, so we cannot answer that question.
11.) Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VO2max in terms of easily obtained quantities. A sample is taken and variables measured are age (years), time necessary to walk 1 mile (mins), and heart rate at the end of the walk (bpm) in addition to the VO2 max uptake. The equation from a multiple regression is (V02) = 0.096*(age) + 0.27*(HR) + 0.069*(time) + 1.293. If a person is 29 years old, blood pressure of 128 bpm, and a walking time of 14 minutes, what is his/her expected maximum oxygen uptake?
a.) We do not know the observations in the data set, so we cannot answer that question.
b.) 22.377
c.) 39.603
d.) 37.017
e.) 38.31
We do not know the observations in the data set, so we cannot answer that question.
b.) 17.3357
c.) 18.1907
d.) -214.6613
e.) -17.3357
13.) Suppose the sales (1000s of $) of a fast food restaurant are a linear function of the number of competing outlets within a 5 mile radius and the population (1000s of people) within a 1 mile radius. The regression equation quantifying this relation is (sales) = 1.39*(competitors) + 6.459*(population) + 9.81. Suppose the sales (in 1000s of $) to be of a store that has 5.571 competitors and a population of 8.465 thousand people within a 1 mile radius are 50.223 (1000s $). You calculate the residual to be 22.006. What is the best interpretation of this residual?
a.) The sales are 22.006 (1000s $) less than what we would expect.
b.) The sales are 22.006 (1000s $) larger than what we would expect.
c.) The sales are 50.223 (1000s $) larger than what we would expect.
d.) The number of competitors are 22.006 stores larger than what we would expect.
e.) The number of competitors are 22.006 stores less than what we would expect.
14.) Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VO2max in terms of easily obtained quantities. A sample is taken and variables measured are age (years), time necessary to walk 1 mile (mins), and heart rate at the end of the walk (bpm) in addition to the VO2 max uptake. The following output is from a multiple regression. Interpret the slope of the age variable.
b.) When age increases by 1 year, V02 decreases by 0.198 L/min, holding all other variables constant.
c.) When age increases by 0.198 years, V02 increases by 1 L/min, holding all other variables constant.
d.) When age decreases by 1 year, V02 increases by 0.198 L/min, holding all other variables constant.
e.) We do not have enough information to say.
15.) Suppose that a researcher wants to predict the weight of female college athletes based on their height, percent body fat, and age. A sample is taken and the following regression table is produced. Based on the F-test alone, what is the correct conclusion about the regression slopes?
b.) All the regression slopes are equal to zero.
c.) We do not have the dataset, therefore, we are unable to make a conclusion about the slopes.
d.) We did not find significant evidence to conclude that at least one slope differs from zero.
e.) All the regression slopes do not equal zero.
Predictor Constant V1 3 CO 31ty load Coef 164.556 6.116 0.019 Stdev 51.19 0.531 0.049 t-ratio 3.21 11.52 0.007428 7.59e-08 0.6979 s 14.905 R-sq 92 , 25 R-sq (adj ) = 90 , 959 Analysis of Variance SOURCE Regression Error Total DE 2 12 MS 15858. 68 222.17 71.38 31717.37 2666.05 34383.41Explanation / Answer
9) (d)
Life time = 164.556 + 6.116 (viscosity) + 0.019(load)
10) (c)
(sales) = 1.798*(competitors) + 5.674*(population) + 5.786.
= 1.798*(2) + 5.674*(15) + 5.786. = 94.492 ((1000s of $))
11) (c)
(V02) = 0.096*(age) + 0.27*(HR) + 0.069*(time) + 1.293.
= 0.096*(29) + 0.27*(128) + 0.069*(14) + 1.293 = 39.603
12) (e)
(time) = 0.096*(distance) + 0.847*(deliveries) - 0.855.
0.096*(249.697) + 0.847*(14.073) - 0.855. = 35.0357 hours
Given time = 17.7 hours
Residual = observed - predicted = 17.7 - 35.0357 = -17.3357
14) (a)
When age increases by 1 year, V02 increases by 0.198 L/min, holding all other variables constant.
Since age coefficient is positive. Therefore V02 is increases by 0.198 L/min
15) (d)
Based on the F-test alone
Here p = 0.124 > 0.05
Hence the model is not significant
i.e.. We did not find significant evidence to conclude that at least one slope differs from zero.
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