1) Based on the data given, estimate the following regressions: Y=a,+a₂X₂ +u₁ Y=X₁ + X₂X₁+U₂₁ Y=B₁+B₂X₂ +B₂X+u Note: Estimate only the coefficients and not the standard errors. a) Is a = B₂ Why or why not? b) Is A, B, Why or why not? = Y X₂ X3 1 1 2 3 2 1 8 3-3
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- Fill the chi square for Cross 1 and Cross 2 from the following data in the attached image: Cross 1: Phenotypes Ratio Observed Expected (O-E)2/E Totals X2 = Cross 2: Phenotypes Ratio Observed Expected (O-E)2/E Totals X2 =Q.2. Because of potential variability in aging due to different castings and segments on the castings, a Latin square design with N=7 was used to investigate the effect of heat treatment on aging. With A= castings, B = Σχ = 297,216.90, segments, C = heat treatments, summary statistics include x... = 3815.8, Σχ = 297,155.01, and 297,200.64, = 297,317.65. Obtain the ANOVA table and test at level .05 the hypothesis that heat treatment has no effect on aging.Given the “data” determined by y = x^3 + (x-1)^2 with x = 0.1, 1.2, 2.3, and 2.9, calculate SSTO, SSR, and R^2. Then recalculate these using x = 0.3, 1, 2.45, and 2.8. Does where you collect your data (i.e., which values of x) appear to impact your interpretation of how good the linear model fits?.
- 6. Medical researchers want to test the theory that the viral load of Covid-19 in children is different than the viral load of the virus in adults. They want to take blood and test the mean viral load in children's blood (uc) and the blood of adults (µA). Hypotheses Ho: Hz: Direction of the extreme:Q1) Interpret the following regression line * y = 10.50-0.18x Your answer Q2) Interpret the following coefficient of determination * r² = 0.69 2 Your answer15) Find the unexplained variation for the paired data. The equation of the regression line for the paired data below is y = 3x. %3D x| 2 4 5 6 y 7 11 13 20 A) 88.75 B) 78.75 C) 14.25 D) 10.00
- It is known that a natural law obeys the quadratic relationship y = ax-. Whatis the best line of the form y = px + q that can be used to model data and minimize Mean-Squared-Error if all of the data points are drawn uniformly atrandom from the domain [0, 1]?Kindly help me with g) h) i) although I know the answer for i) R^2 = 0.7447 and Adjusted R square 0.5989. If you could help interpret it. Here are the answers for the previous ques. for reference. (a) Thus, the multiple linear regression line is, y = (–102.7132) + 0.6054 x1 + 8.9236 x2 + 1.4375 x3 + 0.0136 x4 (b) y = (–102.7132) + 0.6054 (75) + 8.9236 (24) + 1.4375 (90) + 0.0136 (98) = (–102.7132) + 45.405 + 214.1664 + 129.375 + 1.3328 = 287.566 (c) the P-value for the overall model is 0.030302769. It is known that, if the P-value is less than or equal to the level of significance, then reject the null hypothesis. Or else, fail to reject the null hypothesis. Here, the level of significance is 0.05. Hence, the obtained P-value is less than the level of significance. Thus, the null hypothesis is rejected. Therefore, there is enough evidence to claim that the regression model is significant at 5% level of significance. (d) The mean square error is the estimate value of…If the SST=746, the SSE=516, n=472 and the model of interest is y = Bo + B₁x₁ + B₂x12 + B3x3 + B4x4 + B5x5 + u, calculate the root mean squared error. Round to two decimal places.
- A study was carried out to compare the writing lifetimes of four premium brands of pens. It was thought that the writing surface might affect life- time, so three different surfaces were randomly se- tected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., con- stant pressure and a fixed angle). The accompany- ing table shows the two lifetimes (min) obtained for each brand-surface combination. In addition, EEEr = 11,499,492 and EExj, = 22,982,552, Writing Surface 1 2 3 1 709, 659 713, 726 660, 643 Brand 2 668, 685 722, 740 692, 720 of Pen 3 659, 685 666, 684 678, 750 4 698, 650 704, 666 686, 733 4112 4227 4122 4137 5413 5621 5564 16,598 Carry out an appropriate ANOVA, and state your conclusions.Use reg no 134 Q.1 From the set of data X having the values last number of your registration number as X1 is the last digit of your registration number, X2=X1+1, X3=X2+2 and X4=X3+3, then (5+5) I. Show that the sum of the deviations of the observations Xi's from their mean, is equal to zero. II. Show that sum of square of devotion form mean is minimum than the sum of squared devotion from any other arbitrary valueThe following data shows the atmospheric pollutants yi(relative to an EPA standard) at half hour interval xi. Find the equation y=a+bx of the least square line that best fits the data points given by 2,1, 5,2, 7,3, 8,3. Hence predict the atmospheric pollutant at x=6 half hour.