71 45671 18703 22e 16 1 244 model 2 with anova

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1 456.71456.71187.03 < 2.2e-16 ***Residuals 98 239.312.44> # Model 2 with ANOVA #-----------------------------------------------> anova(lm(Y~x-1))DfSum Sq Mean Sq F valuePr(>F)x1 2825.00 2825.001023.8 < 2.2e-16 ***Residuals 99273.182.76> # Model 3 with ANOVA #-----------------------------------------------> x.new <-x+1> anova(lm(Y~x.new))Df Sum Sq Mean Sq F valuePr(>F)x.new1 456.71456.71187.03 < 2.2e-16 ***Residuals 98 239.312.44> # Model 4 with ANOVA #-----------------------------------------------> x.new <-x+1> anova(lm(Y~x.new-1))DfSum Sq Mean Sq F valuePr(>F)x.new1 2855.42 2855.421164.5 < 2.2e-16 ***Residuals 99242.762.458Bo:B.SSEF=SSEOOMSEaER
Problem 2 [35 pts]Consider the following study examining the eects of dierent amounts of THC, the majoringredient in marijuana, injected directly in the brain. The response variable (Y) is locomo-tor activity. In this approach, the researchers run an ANCOVA model (or multiple linearregression model) on the pos-injection scores, partialling out pre-injection dierences. Sucha procedure would adjust for the fact that much of the variability in post-injection activitycould be accounted for by the variability in pre-injection activity. Note that variablesD1throughD4are indicator variables representing the dierent dosage levels andxiis thecontinuous variable pre-injection activity.control.1 micro g (D1).5 micro g (D2)1 micro g (D3)2 micro g (D4)XYXYXYXYXYPrePostPrePostPrePosPrePosPrePos4.341.301.550.937.185.106.942.294.001.443.500.9410.564.448.334.166.104.754.101.11................................................7.352.35..................6.304.84......1.900.939.584.225.542.93n1= 10n2= 10n3= 9n4= 8n5= 10
Part A (25 pts)Run a single hypothesis testing procedure to see if THC dosage levels statistically influencepost-locomotor activity, after controlling for pre-locomotor activity. To receive full credit,state the correct null/alternative pair, compute the test statistic and identify the correctP-value. To complete this exercise, use the
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