x | y | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
2 | 4 | 20.25 | 9.00 | 13.50 |
6 | 7 | 0.25 | 0.00 | 0.00 |
9 | 8 | 6.25 | 1.00 | 2.50 |
9 | 9 | 6.25 | 4.00 | 5.00 |
ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
total sum | 26 | 28 | 33 | 14.000 | 21.000 |
mean | 6.500 | 7.000 | SSxx | SSyy | SSxy |
a)
sample size , n = 4
here, x̅ = Σx / n= 6.50 ,
ȳ = Σy/n = 7.00
SSxx = Σ(x-x̅)² = 33.0000
SSxy= Σ(x-x̅)(y-ȳ) = 21.0
estimated slope , ß1 = SSxy/SSxx = 21.0
/ 33.000 = 0.63636
intercept, ß0 = y̅-ß1* x̄ =
2.86364
so, regression line is Ŷ =
2.863636 + 0.636364
*x
b)
Ho: ß1= 0
H1: ß1╪ 0
n= 4
alpha = 0.05
estimated std error of slope =Se(ß1) = Se/√Sxx =
0.564 /√ 33.00 =
0.0982
t stat = estimated slope/std error =ß1 /Se(ß1) =
0.6364 / 0.0982 =
6.4807
Degree of freedom ,df = n-2= 2
p-value = 0.0230
decison : p-value<α , reject Ho
Conclusion: Reject Ho and conclude that slope
is significantly different from zero
c)
Anova table | |||||
variation | SS | df | MS | F-stat | p-value |
regression | 13.3636 | 1 | 13.3636 | 42.00 | 0.0230 |
error, | 0.6364 | 2 | 0.3182 | ||
total | 14.0000 | 3 |
F=42
p value=0.0230
p-value<α , reject Ho
there is enough evidence that model is significant
d)
R² = (Sxy)²/(Sx.Sy) = 0.9545
Given below are four observations collected in a regression study on two variables x (independent variable)...
A sample of 7 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data. SSR=26, SST=40 Using a 0.05 level of significance, we conclude that there is a significant linear relationship between x and y. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)
A sample of 11 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data. SSR=66, SST=85, summation (x_i-xbar)2=29, summation (x_i-xbar)(y_i-ybar)=50. Calculate the t test statistics to determine whether a statistically linear relationship exists between x and y.
A sample of 6 observations collected in a linear regression study on three variables, x_1(independent variable), x_2(independent variable) and y(dependent variable). The sample resulted in the following data. SSR=72, SST=88 Calculate the F test statistics to determine whether a statistically linear relationship exists between x and y.
Question 10 A sample of 10 observations collected in a regression study on three variables, x_1(independent variable), x_2(independent variable and y(dependent variable). The sample resulted in the following data. SSR=27, SST=36.Using a 0.01 level of significance, we conclude that the regression model is significant overall. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)
The data shown below for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling. X 10 15 11 19 18 17 5 17 18 y 9070 30 8020 30 5060 40 40 a. Develop a simple linear regression equation for these data. b. Calculate the sum of squared residuals, the total sum of squares, and the coefficient of determination c. Calculate the standard error of the estimate. d. Calculate the standard error for...
In the following table is a partial computer output based on a sample of 21 observations, relating an independent variable (X) and a dependent variable: Predictor Coefficient Standard Error Constant 30.139 1.181 X ‐0.2520 0.022 SOURCE SS Regression 1,759.481 Error 259.186 a. Develop the estimated regression line. b. At α = 0.05, test for the significance of the slope. c. At α = 0.05, perform an F‐test. d. Determine the coefficient of determination. e. Determine the coefficient...
Below you are given a partial computer output based on a sample of 21 observations, relating an independent variable (x) and a dependent variable (y). Coefficient Standard Error 1.181 Intercept 30.139 0.022 X -0.252 Analysis of Variance SOURCE SS Regression 1,759.481 259.186 Error Develop the estimated regression line At a 0.05, perform an F test. Determine the coefficient of determination. a. b. c. d. Determine the coefficient of correlation.
Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable (x) and a dependent variable (y). Coefficient Standard Error 7.032 0.184 t-Stat -1.3456 4.1793 Intercept Analysis of Variance SOURCE Regression Error (Residual) 400 138 a. Develop the estimated regression line. b. At a = 0.05, perform an F test. C. Determine the coefficient of determination.
In a simple linear regression study between two variables x ( the independent variable) and y (the dependent variable), a random large sample is collected and the coefficient of correlation r = −.98 is calculated. A)Which of the following conclusion may be made? Group of answer choices x and y are almost perfectly correlated, and y increases as x is increased. x and y are almost perfectly correlated, and y decreases as x is increased. x and y are moderately...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...