# 4.2 ws2

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R ® MAT 133: 4.2 Worksheet #2 4.2 WS #2: Least-Squares Regression Coursepack, p. 323 Name: 1. Itis hypothesized that there are fluctuations in norepinephrine (NE) levels that accompany fluctuations In affect (mood) In those with bipolar affective disorder (manic-depressive iliness). During depressive states, NE levels drop; during manic states, NE levels increase. To test this relationship, researchers measured the level of NE by measuring the metabolite 3-methoxy- 4-hydroxyphenylglycol ("MHPG," measured In micrograms per hour -pg/hr) in the urine of patients experiencing varying levels of mania/depression. Levels of mania/depression during these times were also recorded as polnts on a scale with a low score indicating Increased mania and a high score increased depression. The data from the trials are provided below: MHPG Mood (pg/hr) (pts) 41 22 50 26 58 8 81 10 76 5 53 19 45 26 44 12 37 23 32 28 a. What type of variable "MHPG" (circle one)? Quantitative continuous Qualitative Quantitative discrete b. State the linear regression equation for these data (give 3 decimal places). V=39.033 = o .UoX ¢. Compute the value of the Correlation Coefficient for these data (give 3 decimal places). ~ ©.7 78 d. Describe the strength and direction of the linear relationship between these variables. MOl 0en R e. What is the slope of the regression model? () 2109 What does it mean in this situation? ON }\VC/(&'JC\I,'F N\Hp(j poreeses ) L v l"(l Mooy Efpecky Yo decrtmie L) obowr omed P 0'\"3\- S f. What is the y-intercept of the regression model? 0, Bl (2 What does it mean in this situation? when WHPG 5 0,100 15 @O do Lo 39 POA\ I\ Scanned with CamScanner
Carnvmpuis 4 ik Ko Usingg this model, whist MIHPG lavel do you predict for & patient with s 'Mood' score of 157 s X= 9% .73 Yofn he Using this model, what 'Mood' score do you pradict for a patient with an MHPG level of 707 y= Wony- 041 (79) V= ¥oad- oad (760)= lo. 39 Pors L The patient from part h actually reported a 'Mood' Score of 14, Compute the residusl for this patient, and explaln what this means for your model, f?.St)Wr\ - YAYA ~ Vf@%.""\'/) i g 4l ) eyl AN = 40 A= ke | O 3y U W oppecnl Sy The ¥ o O ey, Y S ) I Give at least two examples of "lurking variables" that could confound the results of this study and prevent the researchers from making the claim th at higher MHPG levels cause mania, ")a\e%'tsl U5 ) o\ Ly £oorers I~.',,» Fyo Scanned with CamScanner