Question

Consider the following observed values: (-5,-2) (-3,1) (0,4) (2,6) (1,3) (1) find the estimated regression line...

Consider the following observed values: (-5,-2) (-3,1) (0,4) (2,6) (1,3)

(1) find the estimated regression line based on the observed data

(2) for each xi, compute fitted value of yi

(3) compute the residuals ei

(4) calculate the coefficient of determination

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

1)The regression line is given as y=3.4+x

It is obtained by the normal equations from the method of least squares

2)Predicted value of y is obtained by substituting the values of x in the equation given in 1.

3)Residual ,ei= actual y - predicted y

4) Coefficient of determination,R2= MSS/TSS = 95.97/105 = 0.914

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Data for two variables, x and y, follow. xi 1   2   3   4   5 yi 5  ...
Data for two variables, x and y, follow. xi 1   2   3   4   5 yi 5   9   7   13   16 (a) Develop the estimated regression equation for these data. (Round your numerical values to two decimal places.) ŷ = 2.20+2.60x Compute the studentized deleted residuals for these data. (Round your answers to two decimal places.) xi yi Studentized Deleted Residual 1 5 2 9 3 7 4 13 5 16
Consider the data. xi 1 2 3 4 5 yi 3 7 5 11 14 The...
Consider the data. xi 1 2 3 4 5 yi 3 7 5 11 14 The estimated regression equation for these data is ŷ = 0.20 + 2.60x. (a) Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2, SST = Σ(yi − y)2, and SSR = Σ(ŷi − y)2. SSE = SST = SSR = (b) Compute the coefficient of determination r2. r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a...
Consider the data. xi 1 2 3 4 5 yi 4 7 6 10 13 The...
Consider the data. xi 1 2 3 4 5 yi 4 7 6 10 13 The estimated regression equation for these data is ŷ = 1.70 + 2.10x. (a) Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2, SST = Σ(yi − y)2, and SSR = Σ(ŷi − y)2. SSE= SST= SSR= (b) Compute the coefficient of determination r2. r2= Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it...
Consider the data. xi 1 2 3 4 5 yi 3 7 4 10 12 The...
Consider the data. xi 1 2 3 4 5 yi 3 7 4 10 12 The estimated regression equation for these data is ŷ = 0.90 + 2.10x. (a)Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2,SST = Σ(yi − y)2,and SSR = Σ(ŷi − y)2. SSE= SST= SSR= (b)Compute the coefficient of determination r2. r2= Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)...
Consider the data. xi 1 2 3 4 5 yi 3 7 4 10 12 The...
Consider the data. xi 1 2 3 4 5 yi 3 7 4 10 12 The estimated regression equation for these data is ŷ = 0.90 + 2.10x. (a) Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2, SST = Σ(yi − y)2, and SSR = Σ(ŷi − y)2. SSE=SST=SSR= (b) Compute the coefficient of determination r2. r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is...
Given are five observations for two variables, and . 1 2 3 4 5 4 6...
Given are five observations for two variables, and . 1 2 3 4 5 4 6 8 12 14 The estimated regression equation for these data is . ^y=1+2.6x a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE=Σ(yi-^yi) SST=Σ(yi-^yi) SSR=Σ(yi-^yi) b. Compute the coefficient of determination r^2 (to 3 decimals). Does this least squares line provide a good fit? c. Compute the sample correlation coefficient (to 4 decimals)
The following data were used in a regression study. Observation 1 2 3 4 5 6...
The following data were used in a regression study. Observation 1 2 3 4 5 6 7 8 9 xi 2 3 4 5 7 7 7 8 9 yi 3 5 4 7 4 6 9 5 11 a) Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.) ŷ = b) Do the assumptions about the error term seem to be satisfied? a) The plot suggests a generally horizontal band of residual...
Select all the statements that are true of a least-squares regression line. 1. R2 measures how...
Select all the statements that are true of a least-squares regression line. 1. R2 measures how much of the variation in Y is explained by X in the estimated linear regression. 2.The regression line maximizes the residuals between the observed values and the predicted values. 3.The slope of the regression line is resistant to outliers. 4.The sum of the squares of the residuals is the smallest sum possible. 5.In the equation of the least-squares regression line, Y^ is a predicted...
The assumption of homoscedasticity requires the residuals (differences between observed and estimated values) to be relatively...
The assumption of homoscedasticity requires the residuals (differences between observed and estimated values) to be relatively similar (homogeneous) across different values of the predictor variables. (T/F) The assumption of normality relates to the distributions of the independent variables; they must be normally distributed. (T/F) If the distribution of residuals (actual value minus estimated value) is negatively skewed with a mean of 5 and a standard deviation of 1, this indicates that (a) the regression line is estimated below the majority...
From the linear regression data used in Chapter 14.2 #3 and carried forward to #17: (40...
From the linear regression data used in Chapter 14.2 #3 and carried forward to #17: (40 points) The sample data and regression coefficients were computed as follows              Item 1 2 3 4 5 Sums Means Yi 7 18 9 26 23 =83 = 16.6 Xi 2 6 9 13 20 =50 = 10 Warning the Xs and Ys are flipped from the way your textbook and my PowerPoint state. But this should not confuse you. From this data above:...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT