Question

***please show clear step with explaination***

2. Let y be the mortality rate (as a percentage of the population of a colony of midge flies living in water with lead concentration : (in ppm). Use the sample data to answer the following questions. (Hint: try not to round too much until your final answer for each part. (a) Find the least-squares line for this data set by computing Bo and 1 (b) Use your answer from part (a) to predict the mortality rate when lead concentration is 500ppm. (c) Compute the mean square error of the data, which is the estimated true variance of the linear regression model. (d) Use your answers from parts (b) and (c) to estimate the probability of mortality rate being greater than 80% in when lead concentration is 500ppm. (e) Compute the coefficient of determination r. What does your answer tell you about your model? Obs. Obs. lead concentration (ppm) 515 535 560 580 600 620 640 lead concentration (ppm) mortality rate 85 66.5 110 60.67 160 66.03 180 74.72 205 73.69 220 66.79 250 67.41 270 69.3 305 69.45 325 71.87 345 70.02 370 72.44 390 74.33 410 73.59 430 72.83 455 76.4 475 73.05 495 75.07 660 680 700 720 mortality rate 83.09 75.45 77.36 76.06 77.1 79.31 75.37 80.33 81.81 86.08 84.11 77.78 90.54 87.3 86.76 84.48 91.63 87.87 740 760 780 800 820 840 850

Answer 1

2)

a)

ŷ = 61.71556 + 0.02991 * X

X Values 85 110 160 180 205 220 Y Values 66.5 60.67 66.03 74.72 73.69 66.79 67.41 69.3 69.45 71.87 70.02 72.44 74.33 73.59 72.83 76.4 73.05 75.07 83.09 Y-Dependent 345 000 390 410 430 455 80 220 360 500 640 X-Independent 780 920 475 495 515 — Regression Line (ỹ = 0.03X + 61.72) Estimate Calculation Summary Sum of X= 17880 Sum of Y = 2756.59 Mean X = 496.6667 Mean Y = 76.5719 Sum of squares (55x) = 1796050 Sum of products (SP) = 53723.7833 Regression Equation = ý = bX+ a b= SPIS5x = 53723.78/1796050 = 0.02991 a = My-bMx = 76.57 - (0.03*496.67) = 61.71556 ỹ = 0.02991x+ 61.71556 X - My -411.6667 -386.6667 -336.6667 -316.6667 -291.6667 -276.6667 -246.6667 -226.6667 -191.6667 - 171.6667 - 151.6667 - 126.6667 - 106.6667 -86.6667 -66.6667 -41.6667 -21.6667 -1.6667 18.3333 38.3333 Y - My -10.0719 - 15.9019 -10.5419 -1.8519 -2.8819 -9.7819 -9. 1619 -7.2719 -7.1219 -4.7019 -6.5519 -4.1319 -2.2419 -2.9819 -3.7419 -0.1719 -3.5219 -1.5019 6.5181 -1.1219 (X - Mx)2 169469.4444 149511.1111 113344.4444 100277.7778 85069.4444 76544.4444 60844.4444 51377.7778 36736.1111 29469.4444 23002.7778 16044.4444 11377.7778 7511.1111 4444.4444 1736.1111 469.4444 2.7778 336.1111 1469.4444 (X-MX/Y - My) 4146.2838 6148.7519 3549. 1213 586.4491 840.5671 2706.338 2259.9463 1648.3074 1365.0394 807.1671 993.7116 523.3796 239.1407 258.4352 249.463 7.1644 76.3088 2.5032 119.4977 -43.0079

Regression Formula: Y= a +bX where slope of trend line is calculated as: (x - )*(y-7) By (x - x)? and the intercept is computed as: b = y-(6,* X)

b) put x = 500

You will get 76.67056

c) From ANOVA table we will get MSE = 25685.8546

Formula to calculate ANOVA

ANOVA Summary Sum of Squares Degrees of Freedom Mean Square Source F-Stat P-Value SS MS Between Groups 3176633.5378 3176633.5378 123.6725 Within Groups 1798009.8238 25685.8546 Total: 4974643.3616

SStotal = Σ-1 (X, - X)? SSwithin = Σ=1 Σ- (X - X;)? SSενεεn = Σ (Χ, - X)?

One-Way ANOVA Table Sum of Squares Mean Square Degrees of Freedom Source F-Stat P-Value DF SS MS Right tail of Between Groups k-1 SSB MSB = SSB / (k-1) F = MSB / MSW F(k-1,N-k) Within Groups N-k SSW MSW = SSW / (N - k) Total: N-1 SST = SSB+SSW

d)

P ( x >80) - P(Z > 80- 7615719) 70-4836 P(Z > 0.458081671) 0,32345 Required. psobru A . 0 | стер 0.45808 e.) g2 = = 0.8197 - ) C4i- g) T0&ci=3){{{4; ~913 le 81.97 0% Total Variation of y can be explained by x.

X-MX -411.667 -386.667 -336.667 - 316.667 -291.667 -276.667 -246.667 -226.667 -191.667 - 171.667 - 151.667 - 126.667 106.667 -86.667 -66.667 -41.667 -21.667 -1.667 18.333 38.333 Y - My - 10.072 - 15.902 - 10.542 -1.852 -2.882 -9.782 -9.162 -7.272 -7.122 -4.702 -6.552 -4.132 -2.242 -2.982 -3.742 -0.172 -3.522 -1.502 6.518 -1.122 (X - MXJ2 169469.444 149511.111 113344.444 100277.778 85069.444 76544.444 60844.444 51377.778 36736.111 29469.444 23002.778 16044.444 11377.778 7511.111 4444.444 1736.111 469.444 2.778 336.111 1469.444 (Y - My)2 101.444 252.872 111.133 3.430 8.306 95.686 83.941 52.881 50.722 22.108 42.928 17.073 5.026 8.892 14.002 0.030 12.404 2.256 42.485 1.259 (X - MXJ/Y - My) 4146.284 6148.752 3549.121 586.449 840.567 2706.338 2259.946 1648.307 1365.039 807.167 993.712 523.380 239.141 258.435 249.463 7.164 76.309 2.503 119.498 -43.008 Result Details & Calculation Key X Values = 17880 Mean = 496.667 (X - Mx)2 = SSx = 1796050 X: X Values Y: Y Values My: Mean of X Values Myi Mean of Y Values X-MX & Y - My Deviation scores (X-MX) & (Y - My Deviation Squared (X-MXJY - My): Product of Deviation Scores Y Values = 2756.59 Mean = 76.572 (Y - My)2 = 55y = 1960.149 X and Y Combined N = 36 (X - MX/Y - My) = 53723.783 R Calculation r = 2(X - My/Y - MX))/ VISSxSS)) r = 53723.783 / ((1796050/1960.149)) = 0.9054 Meta Numerics (cross-check) r = 0.9054 The value of Ris 0.9054.