5 what is the standard error of ˆ β 1 q7 2 stat 331

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Precalculus: Mathematics for Calculus
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Chapter 1 / Exercise 14
Precalculus: Mathematics for Calculus
Redlin/Stewart
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5.What is thestandard error ofˆβ1?
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Precalculus: Mathematics for Calculus
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Chapter 1 / Exercise 14
Precalculus: Mathematics for Calculus
Redlin/Stewart
Expert Verified
STAT 331 - SYDE 334: Applied Linear Modelsa. WriteRcode to produce a matrixY100×3, where each rowyiiid∼ N(µ, V), withµ=125,V=200070003.b. WriteRcode to compute the MLEˆβfor a given design matrixXand response vectory.Q8.The following data consists of monthly measurements relating to the water consump-tion at a manufacturing plant.water<-read.csv("water_usage.txt")head(water)TEMP PROD DAYS PAYR HOUR USAGE1 58.8 710721 12952 30.672 65.2 637322 14168 28.283 70.9 679623 15329 28.914 77.4 920824 16623 29.945 79.3 1479225 19340 30.826 81.0 1456426 18914 38.98The variables are:TEMP: average monthly temperaturePROD: amount of monthly productionDAYS: number of operating days in the monthPAYR: number of people on the monthly payrollHOUR: number of hours the plant was shut down for maintenanceUSAGE: amount of monthly water usagea. WriteRcode to compute the six means and 6×6 sample variance matrix for thevariables in this dataset.b. WriteRcode to fit the linear regression modelUSAGEi=β0+β1TEMPi+β2PRODi+β3HOURi+ǫi,and to extract the MLEˆβ.c. A portion of the regression printout upon fitting the model in (b) to the data is givenbelow:3
Midterm 1: Practice Question SolutionsCoefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 16.3397399 5.65015072.892 0.01260 *TEMP0.1005776 0.06595071.525 0.15120PROD0.0008046 0.00025273.183 0.00719 **HOUR-0.0044910 0.0326203 -0.138 0.89261---Signif. codes: 0’***’0.001’**’0.01’*’0.05’.’0.1

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