2.3*) Graph the following observations of x and y on graph paper. X 12 3 4...
1. (2 points) A research presented data on comprehensive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are: n 14,2y 572, E yi 23,530, Σ Xi-43, Σχ-15742, Σχοϊ-1697.80. Assume that the two variables are related according to the simple linear regression model. Calculate the least squares estimates of the slope and intercept. Estimate σ2 1. (2 points) A research presented data on comprehensive strength x and intrinsic permeability y of various concrete mixes and...
(x -R)2 0 4 (a) Complete the entries in the table. Put the sums in the last row. What are the sample means x and y? (b) Calculate bi and b2 using (2.7) and (2.8) and state their interpretation. (c) Compute )vi. Using these numerical values, show that (d) Use the least squares estimates from part (b) to compute the fitted values of y, and plete the remainder of the table below. Put the sums in the last row. yi...
11. Consider the following set of n-6 observations of x and y given in Table 1 i. Graph the observations in a scatter plot on paper by hand by plotting x on the x-axis and y on the y-axis. Comment on the relationship. Using observations from Table 1, what are the sample means i and-? Using observations from Table 1, calculate the deviations and squared deviations from the sample mean for x: (x 11. iii. -x) and (x )for each...
4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a point on the least squares line, where x-(1/n) Σ-Χί and у-(1/ n) Σ|-1 yi. (Hint: Evaluate the line at x x.) (b) In the suggested exercises, we showed that e,-0 and where e is the ith residual, that is e -y...
4. We have n statistical units. For unit i, we have (xi; yi), for i-1,2,... ,n. We used the least squares line to obtain the estimated regression line у = bo +biz. (a) Show that the centroid (x, y) is a point on the least squares line, where x = (1/n) and у = (1/n) Σ¡ı yi. (Hint: E ) i-1 valuate the line at x = x. (b) In the suggested exercises, we showed that e,-0 and e-0, where...
You may skip part (e) (x -R)2 0 4 (a) Complete the entries in the table. Put the sums in the last row. What are the sample means x and y? (b) Calculate bi and b2 using (2.7) and (2.8) and state their interpretation. (c) Compute )vi. Using these numerical values, show that (d) Use the least squares estimates from part (b) to compute the fitted values of y, and plete the remainder of the table below. Put the sums...
Complete parts (a) through (h) for the data below. x- 40, 50, 60, 70, 80 y-62, 58, 55, 47, 33 B) Find the equation of the line containing the points (50, 58) and (80, 33) y=__x+(__) D) By hand, determine the least-squares regression line The equation of the least-squares regression line is given by ModifyingAbove y with caret equals b 1 x plus b 0y=b1x+b0 where b1 equals r times StartFraction s Subscript y Over s Subscript x EndFractionb1=r•sysx is...
4. Comparing the fit of the regression lines for two sets of data Aa Aa E Examine each of the following scatter diagrams and the corresponding regression lines. Identify which line better fits its data. Graph I Graph 11 Next, calculate a measure of how close the data points are to the regression line. Following are the six pairs of data values for Graph I, along with the regression equation: 5.6 6.6 9.6 y = -0.25 + 1.44x Assignment 14...
Given the data points (xi , yi), with xi 0 1.2 2.3 3.5 4 yi 3.5 1.3 -0.7 0.5 2.7 find and plot (using MATLAB) the least-squares basis functions and the resulting least-squares fitting functions together with the given data points for the case of a) a linear monomial basis p(x)= {1 x}T . b) a quadratic monomial basis p(x)= {1 x x2}T . c) a trigonometric basis p(x)= {1 cosx sinx}T Moreover, determine the coefficients a by the Moore-Penrose...
please show all steps thank you 4. (10 marks) Let βο and βι be the intercept and slope from the regression of y on xi, using n observations Let c1 and c2, with c#0, be constants. Let ß0 and ßl be the intercept and slope from the regression ofciyi on c2xi. Show that ßi-(c1/c2) B\ and Bo -cißo, thereby verifying the claims on units of measurement in Section 2-4. [Hint: Plug the scaled versions of x and y into A-s....