Homework 1 Data and Answer Sheet Lab Section: 1:30 3:30 Set 66 Page 1 Due Tuesday, January 18 Problem A Do all calculations to 4 decimal places to avoid round-off error 1 point Performance Data for Farms Goals for: Farm A Farm B per Farm A Farm B Backfat 0.9 0.75 answer Backfat Fd Conv. Backfat Fd Conv. Feed Conv 25 2.2 1.09 2.77 0.74 2.32 ( x . y ) ... 0.84 2.94 0.66 2.32 Put your answers in the following tables 1.01 2.84 0.70 2.34 Attach your worksheets 1.21 2.78 0.90 2.34 0.76 2.38 0.74 2.57 Farm A Farm B 0.51 2.72 1.03 2.87 Mean Backfat 0.9940 1.08 3.21 1.01 2.75 Mean Feed Conv. 2.7960 . 5310 1.40 3.19 0.80 2.48 Variance For Backfat 0.0625 0.0227 0.92 2.45 0.64 2.57 St. Dev. For Backfat 0.2500 0. 1808 1.12 2.68 0.90 2.26 Variance for Fd Conv. 0.0736 0 0263 Helpful information St. Dev. For Fd Conv. 0.2713 0. 1420 N 10 10 10 10 Covariance BF & FC 0.0348 0. 0120 Sum 9.94 27.96 8.12 24.82 Correlation BF & FC 0.5133 0. 4898 Sum Sq 10 492 78.8384 6.7714 61.9832 Which Farm has a stronger correlation Sum CP. 28. 105 20.2902 between Backfat and Feed Conv. FarmA Tabular T for 95% confidence with 9 Degrees of Regression of FC on BF 0.5570 6. 5264 Freedom is 2.2622 Predicted FC @ .75" BF 2.6601 2. 5047 Do the farms differ performance?] T-Value comparing Backfat 2.0066 Farm with Greater Variation in BF Farm A T-Value comparing Fd Conv. ? 2: 6522 Farm with Greater Variation in FC Farm A Farms differ (95% sure) in Backfat No Farm with more potential for genetic change in BF + arms Farms differ (95% sure) in Fd Conv. yes Farm with more uniformity for BF Farm 13 What percent of the population will satisfy the targeted goal? Z Percent Satisfying Goal Farm A Backfat -0.4 34.5 Farm A Feed Conv. -1.1 13. 4 Farm B Backfat ? - 0.3 34.5 Farm B Feed Conv. -1.4 Graph the Datapoints and Regression line (Fd Conv on Backfat) below.( 1 pts ) Farm A Feed Conversion vs Backfat 3.60 3.40 3.20 3.00 Feed Conversion 2.80 2.60 2.40 2.20 2.00 1.00 1.20 1.40 1.60 1.80 0.40 0.60 0.80 BackfatSet 66 Data and Answer Sheet Page 2 Lab Section: 1:30 3:30 Farm B Feed Conversion vs Backfat 3.60 3.40 3.20 3.00 Feed Conversion 2.80 2.60 2.40 2.20 2.00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 Backfat Problem B 2 points Given the following data on average daily gain (Ibs/day) of 10 bulls: Phenotype Breeding Value Environmental Deviation 3.55 -0.21 -0.34 4.03 0.08 0.01 4.19 -0.19 0.28 3.91 -0. 13 0.06 3.92 0. 14 -0.32 3.9 0.08 -0.12 4.36 0.31 -0.05 4.31 0.28 -0.07 3.85 0.01 0.26 4.18 -0.05 0.13 Count 10 10 10 Sum 40.2 9.02E-17 -0.8 Sum Sq 162. 1446 0.3066 0.4064 Sum of Crossproducts (Pheno & BV) 0.2524 Sum of Crossproducts (Pheno & Env.) 2.9278 Sum of Crossproducts (BV & Env.) -0.0542 Estimate the breeding value of a bull with a growth rate of 4.9 Lbs/day C Note regression of BV on P O. Prediction = Mean of Y+b (x- mear ofx Average Phenotype is 0 .0 Variance of P is Covariance (BVEP ) is 0.0Due Tuesday, January 18 Time to run a mile . etc. etc. etc. Review of Statistics Statistics describe the population - where we are, where we are going Statistics - Homework Statistics - Homework Statistics section at top of Equation Sheet page 1 . Watch out for order of operations Things in parentheses happen first Statistics: . Multiplication/division before addition/subtraction . Operations under the square root happen before you take the square root Sundard Devision - Gx - S, - variance Standard Error - SE . Variance 1+(10-1)(.25*.50+.05) = 1+(9)(.175) = 1+1.575 = 2.575 EXY LXTY . Do calculations to 4 decimal places to avoid Covariance . Covry - Cover Comelation " 7vary. Vary round-off errors. Those round-off errors can accumulate and mess Vary Prediction: " = Y + byx(X -X) up the result. Varya + Varys Show your work. Hand in a sheet with calculations. Do ar culauditors to # decimal places to avoid round of error wifeamonon Data for Farms Farm B 0.75 Food Com 277 255 Put your stivers in the blowing Habana Sums - "Helpful Information" box Attach your wars diets. Fairn Note: this is not Mean Bachfat SX SX Mean Fired Comm. the same as: Verlarico For Bickiat ([* ) OL Dev. For Backfat Variance Kir Fa Cory Sum Sum of Squares St Dov. For Fd Cory. (Sum Sq.) Correlation BF & FC Which Fara has as site If there are three X's with values 1, 2, and 3 then: Deepen Backfat and Feed Com Tebauder T for $5% confidence with ! Degrees Hagration of FC on BF sendont is 2.3021 2 720 Farm with Greater Volition in BF [x =1+2+3 =6 Ex? = 12 + 23 + 32 = 1+4+9 = 14 amos differ $5% survi in Backlan ams differ [13% surol in Fd Cons. Form win more uniformity for BF What percent of The populationwl wibly the to ed goal ([x) =(1+2+3)? =62 =36 Farn A BackdalPrediction Questions on Variation Y = Y + byx(X=X) Amount of Variation = the Variance for the trait Means Uniformity means there is little variation - Calculates the points on the regression line Animals that are uniform look the same or have similar performance . Actual data points Potential for genetic change - Predicted points If there is no variation, you can't change the population bigger variation = mone change 0 = no change what back fat you went to predict T-Values T-Values Are two means different from each other? Do the farms differ in performance? Is it significant? Look at the absolute value of t (ignore sign) t= - Y 1 - Y2 vary, + Varyz SE diff SEdiff = Compare to 2.2622 nz If absolute value of t > 2.2622 then the means for the two farms are significantly different, you are 95% Numerator of t sure they're different. Difference between the means for trait Y at the 2 farms Denominator of t 2. 5 = sig. different = Standard Error of the difference between the means Has the variances for trait Y on the two farms 2. 1 = not diffement Z Z Table - Area of Normal Distribution Normal distribution to calculate % of population satisfying a goal Goals are in the upper right of the homework (page 1) Z = (Target - Mean) / Standard Deviation Number of standard deviations the target is above/below the mean Less is Best (Dark) % Desired " Undesired Z negative Z positive Bigger is Better (Light) % Undesired %% Desired Area s Target Area > Target -1.0 0.159 0.841 below +1.0 0.841 0.159 Moan See handout for complete table. Round Z to 1 decimal place (e.g., 2.1). For both traits in the homework, lower is better. lower = bether want acaiProblem B Making the Graph Given data for 10 bulls, one trait - ADG 3 values for each bull - Phenotype, Breeding Value, Use the data points for Farm A. Add the regression line - Environmental Dev. Sums, Sums of Squares, Sums of Crossproducts are That's a specific line, not an approximate line that looks good. already calculated Go back to the slide on Prediction. * Each predicted point is on the regression line. You have another bull with a particular growth rate One is already calculated for you. (phenotype) need to estimate the Breeding Value . What formula do you need to answer that? Which is X and which is Y? -Boudng value havea phenotype Hints! Homework Ground Rules . Variance must be + Please use the homework sheet. If you do not use Standard deviation must be + it, please have a sheet that looks like it, and make . Correlation must be between -1 and +1 answers obvious. . On a graph, the location of the regression line Homeworks can always be turned in early. should make sense given where the data points are Homeworks can be turned in late, 20% (5 pts) located deducted for each 24 hours late. The grader will be looking ONLY at final answers. In other words - your answers should make sense! HW can be handed back to me for partial credit. Work MUST be included with your original submission. If they don't you might want to try again@ It helps if it is organized and labeled.Formulas Used in ANSC 311 Statistics: Mean = X = _X n Variance = Vx = of = $3 = EX2 _([X)2 n-1 Standard Deviation = Oy = Sy = VVariance Variance Standard Error = SE = n EXY_EXEY Covariance = Covxy n COVXY Correlation = n-1 Varx Vary Regression: byx = COVXY Prediction: Y = Y + byx(X - X) Varx Z = Target-Mean Y1 - Y 2 Varyz t= Vary1 + Std.Dev. SEdifference SEdifference n1 n2 Population Genetics: p+ q=1 (Ps + qs) (PD + qD) = 1 Mean = _ (Frequency x Value) Effective Number = Ne = 4N m Nf Nm + Nf Drift Standard Deviation = pq 2Ne Pop. Mean = P = p2P11 + 2pqP12 + q2P22 Offspring Phenotype = (BVsire + BVdam) /2 Genetic Value = Gij = Pij - P Breeding Value = Ajj = a; + aj Allelic Effects (a's): a1 = pG11 + qG12 a2 = PG12 + qG22 Selection: Dominant allele desired: Recessive allele desired: (1-hs)2pq+2(1-s)q2 (1-hs)2pq+2q2 q'= 2[1p2+(1-hs)2pq+(1-s)q2] 9 2[(1-s)p2+(1-hs)2pq+1q2] Aq = q'- q When h=0 (complete dominance and dominant allele desired) Aq =-sq p/(1-sq2) When h=1 (complete dominance and recessive allele desired) Aq = sq p/[1-s(1-q2)] Qualitative Traits: Testing for carrier genotypes, where n = number of offspring observed: Level of Confidence = 1 - (Prob. of desired phenotype)" = 1 - (1 - qsd)" In(1-Level of Confidence) 1= In(1-qsqd) Genetic Model: P = A + D + I+ Ep + ET Heritability = h2 = VA/VP H2 = h broad sense = VG/VP Repeatability = R = (VG+VEP)/VPANSC 311 Normal Distribution to Calculate % of Population Satisfying Goal. Percent of a Population Above or Below a Targeted Goal Z = (Target - Mean)/Standard Deviation Target Target Mean Mean Area of normal distribution Less is Best (Dark) % Desired % Undesired % Desired % Undesired Bigger is Better % Undesired % Desired % Undesired % Desired (Light) Z Area s Target Area > Target Z Area S Target Area > Target -3.1 0.001 0.999 0.0 0.500 0.500 -3.0 0.001 0.999 0.1 0.540 0.460 -2.9 0.002 0.998 0.2 0.579 0.421 -2.8 0.003 0.997 0.3 0.618 -2.7 0.382 0.003 0.997 0.4 0.655 0.345 -2.6 0.005 0.995 0.5 0.691 0.309 -2.5 0.006 0.994 0.6 0.726 -2.4 0.274 0.008 0.992 0.7 0.758 0.242 -2.3 0.011 0.989 0.8 0.788 -2.2 0.212 0.014 0.986 0.9 0.816 0.184 -2.1 0.018 0.982 1.0 0.841 0.159 -2.0 0.023 0.977 1.1 0.864 0. 136 -1.9 0.029 0.971 1.2 0.885 0.115 -1.8 0.036 0.964 1.3 0.903 0.097 -1.7 0.045 0.955 1.4 0.919 0.081 -1.6 0.055 0.945 1.5 0.933 0.067 -1.5 0.067 0.933 1.6 0.945 0.055 -1.4 0.081 0.919 1.7 0.955 0.045 -1.3 0.097 0.903 1.8 0.964 0.036 -1.2 0. 115 0.885 1.9 0.971 0.029 -1.1 0. 136 0.864 2.0 0.977 0.023 -1.0 0. 159 0.841 2.1 0.982 0.018 -0.9 0. 184 0.816 2.2 0.986 0.014 -0.8 0.212 0.788 2.3 0.989 0.011 -0.7 0.242 0.758 2.4 0.992 0.008 -0.6 0.274 0.726 2.5 0.994 0.006 -0.5 0.309 0.691 2.6 0.995 0.005 -0.4 0.345 0.655 2.7 0.997 0.003 -0.3 0.382 0.618 2.8 0.997 0.003 -0.2 0.42 0.579 2.9 0.998 0.002 -0.1 0.460 0.540 3.0 0.999 0.001 0.0 0.500 0.500 3.1 0.999 0.001Sum of Crossproducts Single trait statistics SumCP Mean = Ex Same units as the trait, e.g. inches H" Variance = Ex - Exy Multiply each pair of numbers together and add 8-1 Units squared, e.g. Inches? them up. (Backfat * Feed conversion for animal 1) Standard Deviation = vVariance Same units as the trait + (Backfat * Feed conversion for animal 2) + ... + (Backfat * Feed conversion for animal 10) Mean = J = X Variance = Var = V = $3 =q? So SD = S=G Covariance Correlation (Sum of X) Correlation = COVXY EXY _ EXEY- Varx Vary Covariance =/ n times n- 1 (Sum of Y) No units. Range -1 to 1. Sum of crossproducts 0 means the traits are not correlated (no relationship between them). Units = inches * Ibs feed/lb gain Which isn't very easy to interpret! Stronger correlation = further from zero (ignoring the sign) Correlations of +.2 and -.8 -- which is stronger? -. 2 Correlation Regression Relationship between traits - DOES NOT imply cause and effect Regression byx =- COVXY = slope of Varx the line There was a strong positive correlation between banana imports and birth rate in the U.S. Y.X means Y on X during and immediately following World War II Slope = change in Y per unit of change in x different cause Regression of Feed Conversion on Backfat Units = (Ibs feed/lb gain) / inch of backfat Predict feed conversionFeed Co 2.60 2.40 2.20 2.00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 Backfat This study source was downloaded by 100000810223659 from CourseHero.com on 01-17-2022 17:55:28 GMT -06:00 https://www.coursehero.com/file/85832872/HW01-Key-for-set-52pdf ANSC 311 Homework 1 Key Set 52 Page 2 Farm B Feed Conversion vs Backfat 3.60 3.40 3.20 3.00 Feed Conversion 2.80 2.60 2.40 2.20 2.00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 Backfat Problem B 2 points Given the following data on average daily gain (Ibs/day) of 10 bulls: Phenotype Breeding Value Environmental Deviation 3.73 0.35 -0.02 4.18 0.13 -0.05 3.93 -0.01 -0.16 4.31 0.14 0.07 3.87 0.24 0.01 4.46 0.25 0.11 4.64 0.23 0.31 4.1 0.05 -0.05 3.92 0.16 -0.02 3.99 -0.04 -0.07 Count 10.00 10.00 10.00 Sum 41.13 0.00 0.13 Sum Sq 169.9009 0.3618 0.1495 Sum of Crossproducts (Pheno & BV) 0.4736 Sum of Crossproducts (Pheno & Env.) 0.7943 Sum of Crossproducts (BV & Env.) 0.1118 Estimate the breeding value of a bull with a growth rate of 4.9 Lbs/day 0.5083 Note Regression of BV on P 0.64593 Prediction =Mean of Y+b(X-mean of X) Average Phenotype is 4.113 Variance of P is 0.08147 Covariance (BV&P) is 0.05262ANSC 311 Homework Key Set 52 Page 1 Problem A Do all calculations to 4 decimal places to avoid round-off error 1 point Performance Data for Farms Goals for: Farm A Farm B per Farm A Farm B Backfat 0.9 0.75 answer Backfat Fd Conv. Backfat Fd Conv. Feed Conv. 2.5 2.2 1.09 2.77 .89 2.70 0.84 2.94 0.79 2.80 Put your answers in the following tables 1.01 2.84 0.90 2.55 Attach your worksheets 1.21 2.78 0.62 2.32 0.76 2.38 0.99 2.61 Farm A Farm B 0.51 2.72 0.97 2.44 Mean Backfat 0.9940 0.8000 1.08 3.21 0.84 2.46 Mean Feed Conv. 2.7960 2.5310 1.40 3.19 0.68 2.37 Variance For Backfat 0.0625 0.0227 0.92 2.45 0.53 2.38 St. Dev. For Backfat 0.2500 0.1508 1.12 2.68 0.79 2.68 Variance for Fd Conv. 0.0736 0.0263 Helpful information St. Dev. For Fd Conv. 0.2713 0.1620 N 10 10 10 10 Covariance BF & FC 0.0348 0.0120 Sum 9.94 27.96 8 25.31 Correlation BF & FC 0.5133 0.4898 Sum Sq. 10.4428 78.8384 6.6046 64.2959 Which Farm has a stronger correlation Sum CP. 28.1055 20.3557 between Backfat and Feed Conv. Farm A Tabular T for 95% confidence with 9 Degrees of Regression of FC on BF 0.5570 0.5264 Freedom is 2.2622 Predicted FC @ .75" BF 2.6601 2.5047 Do the farms differ performance? T-Value comparing Backfat 2.1014 Farm with Greater Variation in BF Farm A T-Value comparing Fd Conv. 2.6522 Farm with Greater Variation in FC Farm A Farms differ (95% sure) in Backfat No Farm with more potential for genetic change in BF Farm A Farms differ (95% sure) in Fd Conv. Yes Farm with more uniformity for BF Farm B What percent of the population will satisfy the targeted goal? Z Percent Satisfying Goal Farm A Backfat -0.4 34.5 Farm A Feed Conv. -1.1 13.6 Farm B Backfat -0.3 38.2 Farm B Feed Conv. -2 2.3 Graph the Datapoints and Regression line (Fd Conv on Backfat) below.( 1 pts ) Farm A Feed Conversion vs Backfat 3.60 3.40 3.20 3.00 Feed Conversion 2.80 2.60 2.40 2.20 2.00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 Backfat This study source was downloaded by 100000810223659 from CourseHero.com on 01-17-2022 17:55:28 GMT -06:00 https://www.coursehero.com/file/85832872/HW01-Key-for-set-52pdf/ ANSC 311 Homework 1 Key Set 52 Page 2 Farm B Feed Conversion vs Backfat 3.60 3.40 3.20