Complete the assignment. Additional PDFs included for questions 7 and 8. They have tables for the 2 questions
Bios 18 Nurs 717 HW #5 Question 1) The following is information about the number of hour freshman nursing students studies and the grade that they receive in Statistics course: (Each parts 3 points total 12 points). You can calculate by hand or use following output to answer the questions. Number of hours study (x): 1, 2, 3, 3, 4, 4, 5, 5, 6, 7 Grade (Y):60, 65, 75, 74, 80, 80, 85, 85, 90, 95 a) What does the scatter plot show? 1. It seems there is positive linear association between number of hours study and grade. 2. It seems there is negative linear association between number of hours study and grade. 3. It seems there is no linear association between number of hours study and grade. 4. None of above b) What is the sample Pearson correlation coefficient? 1. .80 2. .70 3. .992 4. -.65 c) What is the T statistic to Test H0: ρ =0 at alpha=.05? 1. 11.20 2. 5.67 3. 13.56 4. 22.18 d) What is your conclusion to Test H0: ρ =0 at alpha=.05? 1. Yes, Since T statistics is greater T value from table, we reject H0 and conclude that there is linear positive relationship between number of hours study and grade. 2. No, Since T statistics is less T value from table, we cannot reject H0 and cannot conclude that there is linear positive relationship between number of hours study and grade. 3. Use the following table for your calculation (You need to find Sxx, Sxy, and Syy to compute r by using the information from the following table): Obs x y Xsq Ysq XY 1 1 60 1 3600 60 2 2 65 4 4225 130 3 3 75 9 5625 225 4 3 74 9 5476 222 5 4 80 16 6400 320 6 4 80 16 6400 320 7 5 85 25 7225 425 8 5 85 25 7225 425 9 6 90 36 8100 540 10 7 95 49 9025 665 40 789 190 63301 3332 Pearson Correlation Coefficients, N = 10 Prob > |r| under H0: Rho=0 x y x number of hours study 1.00000 0.99217 <.0001 y="" grade="" 0.99217=""><.0001 1.00000="" question="" 2)="" the="" following="" is="" the="" information="" on="" anxiety="" (y)="" and="" physical="" activity="" (x)="" output="" for="" 10="" subjects.="" the="" higher="" score="" for="" anxiety="" means="" more="" anxious="" and="" higher="" score="" for="" physical="" activity="" means="" more="" active.="" (each="" part="" 3="" points="" total="" 15="" points).="" you="" can="" calculate="" by="" hand="" or="" use="" following="" output="" to="" answer="" the="" questions.="" subject="" anxiety="" physical="" activity="" 1="" 20="" 90="" 2="" 21="" 92="" 3="" 60="" 55="" 4="" 30="" 65="" 5="" 24="" 95="" 6="" 50="" 62="" 7="" 45="" 60="" 8="" 30="" 70="" 9="" 40="" 66="" 10="" 62="" 50="" a)="" what="" does="" the="" scatter="" plot="" show?="" 1.="" it="" seems="" there="" is="" positive="" linear="" association="" between="" anxiety="" (y)="" and="" physical="" activity="" (x).="" 2.="" it="" seems="" there="" is="" negative="" linear="" association="" between="" anxiety="" (y)="" and="" physical="" activity="" (x).="" 3.="" it="" seems="" there="" is="" no="" linear="" association="" between="" anxiety="" (y)="" and="" physical="" activity="" (x).="" 4.="" none="" of="" above="" b)="" what="" is="" he="" sample="" pearson="" correlation="" coefficient?="" 1.="" -.899="" 2.="" .70="" 3.="" .99="" 4.="" -.65="" c)="" what="" is="" the="" t="" statistics="" to="" test="" h0:="" ρ="0" at="" alpha=".05?" 1.="" 11.20="" 2.="" -5.80="" 3.="" 13.56="" 4.="" -2.18="" d)="" what="" is="" your="" conclusion="" to="" test="" h0:="" ρ="0" at="" alpha=".05?" 1.="" yes,="" since="" absolute="" value="" of="" t="" statistics="" is="" greater="" t="" value="" from="" table,="" we="" reject="" h0="" and="" conclude="" that="" there="" is="" linear="" negative="" relationship="" between="" anxiety="" and="" physical="" activity.="" 2.="" no,="" since="" absolute="" value="" of="" t="" statistics="" is="" less="" t="" value="" from="" table,="" we="" cannot="" reject="" h0="" and="" cannot="" conclude="" that="" there="" is="" linear="" negative="" relationship="" between="" anxiety="" and="" physical="" activity.="" e)="" what="" is="" the="" sample="" spearman="" correlation="" coefficient?="" 1.="" -.70="" 2.="" .75="" 3.="" .99="" 4.="" -.90="" use="" the="" following="" table="" for="" your="" calculation="" (you="" need="" to="" find="" sxx,="" sxy,="" and="" syy="" to="" compute="" r="" by="" using="" the="" information="" from="" the="" following="" table):="" obs="" x="" y="" xsq="" ysq="" xy="" 1="" 90="" 20="" 8100="" 400="" 1800="" 2="" 92="" 21="" 8464="" 441="" 1932="" 3="" 55="" 60="" 3025="" 3600="" 3300="" 4="" 65="" 30="" 4225="" 900="" 1950="" 5="" 95="" 24="" 9025="" 576="" 2280="" 6="" 62="" 50="" 3844="" 2500="" 3100="" 7="" 60="" 45="" 3600="" 2025="" 2700="" 8="" 70="" 31="" 4900="" 961="" 2170="" 9="" 66="" 40="" 4356="" 1600="" 2640="" 10="" 50="" 62="" 2500="" 3844="" 3100="" 705="" 383="" 52039="" 16847="" 24972="" pearson correlation coefficients, n =" 10" prob =""> |r| under H0: Rho=0 X y X physical activity 1.00000 -0.89964 0.0004 y anxiety -0.89964 0.0004 1.00000 Use and complete this table to calculate spearman correlation: Subject Anxiety Physical activity Rank for Anxiety Rank for Physical Activity Di D2 1 20 90 2 21 92 3 60 55 4 30 65 5 24 95 6 50 62 7 45 60 8 31 70 9 40 66 10 62 50 Total Spearman Correlation Coefficients, N = 10 Prob > |r| under H0: Rho=0 X y X physical activity 1.00000 -0.90303 0.0003 y anxiety -0.90303 0.0003 1.00000 Question 3) The following is the correlation matrix for the variables Anxiety (Y), physical activity (X1) and smoking (X2). (Each parts 3 points total 9 points) a) What is the highest correlation in this table? 1. Between Anxiety and Physical 2. Between Anxiety and Smoking 3. Between Physical and Smoking b) What is the partial correlation between anxiety and physical activity after controlling for smoking? (Tips: Here your outcome is anxiety (your y), your independent variable is physical activity (X1 or 1), and smoking as controlling variable (X2 or 2). Thus, for partial correlation you have three correlations: -.60 anxiety with physical (YX1 or Y1), .80 anxiety and smoking (YX2 or y2), and -.40 physical and smoking (X1X2 or 12). You replace in the partial formula) 1. -.51 2. -.31 3. -.24 4. .70 c) What is the semi correlation between anxiety and physical activity after controlling for smoking? (Tips: Form above problem you only use the same numerator in b part and only correlation for -.40 physical and smoking in denominator). 1. -.51 2. -.31 3. -.24 4. .70 Note: For this Assignment you must use the SAS Output to answer questions. Question 4) The following is information about the number of hour freshman nursing student studies and the grade that they receive in Statistics course: (Each part 3 points total 18 points) Number of hours study (x): 1, 2, 3, 3, 4, 4, 5, 5, 6, 7 Grade (Y):60, 65, 75, 74, 80, 80, 85, 85, 90, 95 a) Fit a model of grade as predicted by number of hours study (write the prediction equation). 1. Prediction Equation: Grade = 55.43 - 5.87 X (Number of hours Study) 2. Prediction Equation: Grade = 55.43 + 5.87 X (Number of hours Study) b) Explain residual versus predicted plot: 1. The plots (residual versus predicted value) show that there is no pattern suggesting specification of errors. 2. The plots (residual versus predicted value) show that there is some pattern suggesting specification of errors. c) Test if your slope is significant (H0 = beta =0). 1. Since our P value <.0001 is="" less="" than="" alpha="" .05="" we="" reject="" null="" and="" conclude="" that="" the="" slope="" is="" different="" from="" 0.="" this="" means="" there="" is="" linear="" relationship="" between="" hours="" of="" study="" and="" grade.="" 2.="" since="" our="" p="" value=""><.0001 is="" less="" than="" alpha="" .05="" we="" fail="" to="" reject="" null="" and="" cannot="" conclude="" that="" the="" slope="" is="" different="" from="" 0.="" this="" means="" there="" is="" no="" linear="" relationship="" between="" hours="" of="" study="" and="" grade.="" d)="" what="" is="" the="" r2="" and="" adjusted="" r2="" from="" anova="" table?="" 1.="" .89="" 2.="" .78="" 3.="" .85="" 4.="" .98="" e)="" what="" is="" the="" 95%="" confidence="" interval="" for="" slope?="" 1.="" 5.27="" and="" 6.47="" 2.="" 3.1="" and="" 5.3="" 3.="" 11.30="" and="" 13.54="" 4.="" none="" of="" above="" f)="" what="" would="" be="" the="" grade="" for="" someone="" who="" study="" 3.5="" hours?="" 1.="" 65.98="" 2.="" 75.98="" 3.="" 98.75="" 4.="" 72.35="" sas="" output:="" number="" of="" observations="" read="" 10="" number="" of="" observations="" used="" 10="" analysis="" of="" variance="" source="" df="" sum of="" squares="" mean="" square="" f="" value="" pr =""> F Model 1 1032.53333 1032.53333 504.70<.0001 error="" 8="" 16.36667="" 2.04583="" corrected="" total="" 9="" 1048.90000="" root="" mse="" 1.43033="" r-square="" 0.9844="" dependent="" mean="" 78.90000="" adj="" r-sq="" 0.9824="" coeff="" var="" 1.81283="" parameter="" estimates="" variable="" label="" df="" parameter="" estimate="" standard="" error="" t value="" pr =""> |t| Standardized Estimate Squared Semi-partial Corr Type II Squared Partial Corr Type II Intercept Intercept 1 55.43333 1.13829 48.70<.0001 0="" .="" .="" x="" number="" of="" hours="" study="" 1="" 5.86667="" 0.26114="" 22.47=""><.0001 0.99217="" 0.98440="" 0.98440="" question="" 5)="" the="" following="" is="" the="" information="" on="" anxiety="" (y)="" and="" physical="" activity="" (x)="" output="" for="" 10="" subjects.="" the="" higher="" score="" for="" anxiety="" means="" more="" anxious="" and="" higher="" score="" for="" physical="" activity="" means="" more="" active.="" (each="" part="" 3="" points="" total="" 15="" points)="" subject="" anxiety="" physical="" activity="" 1="" 20="" 90="" 2="" 21="" 92="" 3="" 60="" 55="" 4="" 30="" 65="" 5="" 24="" 95="" 6="" 50="" 62="" 7="" 45="" 60="" 8="" 30="" 70="" 9="" 40="" 66="" 10="" 62="" 50="" a)="" fit="" a="" model="" of="" anxiety="" as="" predicted="" by="" physical="" activity="" (write="" the="" prediction="" equation).="" 1.="" prediction="" equation:="" anxiety="99.54" +="" 0.87="" x="" (physical="" activity)="" 2.="" prediction="" equation:="" anxiety="99.54" -="" 0.87="" x="" (physical="" activity)="" b)="" explain="" residual="" versus="" predicted="" plot.="" 1.="" the="" plots="" (residual="" versus="" predicted="" value)="" show="" that="" there="" is="" no="" pattern="" suggesting="" specification="" of="" errors.="" 2.="" the="" plots="" (residual="" versus="" predicted="" value)="" show="" that="" there="" is="" some="" pattern="" suggesting="" specification="" of="" errors.="" c)="" test="" if="" your="" slope="" is="" significant="" (h0="beta" =0).="" 1.="" since="" our="" p="" value=""><.0001 is="" less="" than="" alpha="" .05="" we="" reject="" null="" and="" conclude="" that="" the="" slope="" is="" different="" from="" 0.="" this="" means="" there="" is="" linear="" relationship="" between="" physical="" activity="" and="" anxiety.="" 2.="" since="" our="" p="" value=""><.0001 is less than alpha .05 we fail to reject null and cannot conclude that the slope is different from 0. this means there is no linear relationship between physical activity and anxiety. d) what is the r2 and adjusted r2? 1. .81 and .79 2. .70 and .76 3. .81 and .70 4. .99 is="" less="" than="" alpha="" .05="" we="" fail="" to="" reject="" null="" and="" cannot="" conclude="" that="" the="" slope="" is="" different="" from="" 0.="" this="" means="" there="" is="" no="" linear="" relationship="" between="" physical="" activity="" and="" anxiety.="" d)="" what="" is="" the="" r2="" and="" adjusted="" r2?="" 1.="" .81="" and="" .79="" 2.="" .70="" and="" .76="" 3.="" .81="" and="" .70="" 4.="">