Homework Answers
Answer:
From the given data,
a)
| Xi | Yj | Xi^2 | XiYj |
| 2 | 3 | 4 | 6 |
| 5 | 2 | 25 | 10 |
| 3 | 4 | 9 | 12 |
| 8 | 0 |
64 |
0 |
| sum=18 | 9 | 102 | 28 |
b)
1=SSxy/SSxx=-12.5/21=−0.5952
0=Y-X1=2.25-(4.5*-0.5952)=4.9286
c)yˆ = β0 + β1X
Y=4.9286-0.5952X
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 5 10 14 (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.
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) i...
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...
Consider the following information regarding a response variable y and an explanatory variable x. x⎯⎯=8∑(xi−x⎯⎯)2=696 ∑(xi−x⎯⎯)(yi−y⎯⎯)=−346x¯=8∑xi-x¯2=696...
Consider the following information regarding a response variable y and an explanatory variable x. x⎯⎯=8∑(xi−x⎯⎯)2=696 ∑(xi−x⎯⎯)(yi−y⎯⎯)=−346x¯=8∑xi-x¯2=696 ∑xi-x¯yi-y¯=-346 y⎯⎯=8Σ(yi−y⎯⎯)2=185Σ(yi−yˆ)2=13n=25y¯= 8 Σ(yi− y¯)2 = 185 Σ(yi− y^)2=13n= 25 a. Calculate b0 and b1.b. What is the sample regression equation? Predict y if x equals 10. c. Calculate the standard error of the estimate. d. Calculate and interpret the coefficient of determination.
1. (2 points) A research presented data on comprehensive strength x and intrinsic permeability y ...
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...
Given are five observations for two variables, x and y. xi 3 12 6 20 14...
Given are five observations for two variables, x and
y.
xi
3
12
6
20
14
yi
50
45
55
15
15
(d) Develop the estimated regression equation by computing the
values of b0 and b1 using b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and b0 = y − b1x.
ŷ =
(e) Use the estimated regression equation to predict the value
of y when x = 9.
Observation 1 2 3 4 5 6 7 8...
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 poin...
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...
Fifteen houses rented recently in a certain county provided the data: size of the house x...
Fifteen houses rented recently in a certain county provided the data: size of the house x (in sq.ft.) and the monthly renty (in thousands of dollars). The sample data are summarized by the following information: n = 15. Ex = 16,560, y = 21.685, Exy = 28,474.85. Ex2 = 22,557,866, y2 = 36.93, 6505 x 52,400 The following sums were also computed: SSxy=4,534.61, SSxx = 4,275,626, SSyy = 5.5807 1. Which of the following is the slope of the least...
Given are five observations for two variables, x and y. xi 4 8 14 16 18...
Given are five observations for two variables, x and y. xi 4 8 14 16 18 yi 58 52 45 24 11 The estimated regression equation for these data is y= 75.06 - 3.09x. A. Compute SSE, SST, and SSR using the following equations (to 2 decimal). B.Compute the coefficient of determination r2 (to 3 decimals). The least squares line provided an (good/bad) fit; ---------% of the variability in y has been explained by the estimated regression equation (to 1...
xi 1 2 3 4 5 yi 4 7 6 12 15 d. Develop the estimated...
xi 1 2 3 4 5 yi 4 7 6 12 15 d. Develop the estimated regression equation by computing the values of b0 an b1 y=_____ +______x e. Use of estimated regression equation to predict the value of y when x =5 y=_____
(x -R)2 0 4 (a) Complete the entries in the table. Put the sums in the...
(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...
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...
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...
Given are five observations for two variables, x and
y.
xi
3
12
6
20
14
yi
50
45
55
15
15
(d) Develop the estimated regression equation by computing the
values of b0 and b1 using b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and b0 = y − b1x.
ŷ =
(e) Use the estimated regression equation to predict the value
of y when x = 9.
Observation 1 2 3 4 5 6 7 8...
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...
Fifteen houses rented recently in a certain county provided the data: size of the house x (in sq.ft.) and the monthly renty (in thousands of dollars). The sample data are summarized by the following information: n = 15. Ex = 16,560, y = 21.685, Exy = 28,474.85. Ex2 = 22,557,866, y2 = 36.93, 6505 x 52,400 The following sums were also computed: SSxy=4,534.61, SSxx = 4,275,626, SSyy = 5.5807 1. Which of the following is the slope of the least...
(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...
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