In a simple linear regression, the following information is given: \(\bar{x}=-25 ; \bar{y}=56 ; \sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\right.\) \(\bar{y})=1250 ; \sum\left(x_{i}-\bar{x}\right)^{2}=711\)
a. Calculate \(b_{1}\)
b. Calculate \(b_{0}\)
c. What is the sample regression equation? Predict \(y\) if \(x\) equals \(-20\).
In a simple linear regression, the following information is given: x−x− = −39; y− y− = 40; Σ(xi−x− )(yi− y−)= −840;Σ(xi−x− )(yi− y−)= −840; Σ(xi− x−)2= 718Σ(xi− x−)2= 718 a. Calculate b1. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) b1 b. Calculate b0. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) b0 c-1. What is the sample regression equation? (Negative value should be...
(Based on Stock & Watson "Introduction to Econometrics" 6th ed., Exercise 5.8.) Suppose that \(\left(Y_{i}, X_{i}\right)\) satisfy the simple linear regression assumptions. In addition, \(u_{i}\) is \(N\left(0, \sigma_{u}^{2}\right)\) and is independent of \(X_{i}\). A sample of size \(n=30\) yields$$ \hat{Y}_{i}=43.2+61.5 X_{i}, n=30, R^{2}=0.54 . $$$$ (10.2)(7.4) $$(a) Construct a \(95 \%\) confidence in(a) Construct a \(95 \%\) confidence interval for \(\beta_{0}\).(b) Test \(H_{0}: \beta_{1}=55\) v.s. \(H_{1}: \beta_{1} \neq 55\) at the significance level \(5 \%\).(c) Test \(H_{0}: \beta_{1}=55\) v.s. \(H_{1}:...
QUESTION 1In a simple linear regression model, the intercept of the regression line measuresa.the change in Y per unit change in X.b.the change in X per unit change in Y.c.the expected change in Y per unit change in X.d.the expected change in X per unit change in Y.e.the value of Y when X equals 0.f.the value of X when Y equals 0.g.the average value of Y when X equals 0.h.the average value of X when Y equals 0.QUESTION 2In a...
QUESTION 20 In a simple linear regression model the data is given as X: 1, 2, 3, 4; Y: 7, 10, 9, 12. The estimated intercept is 6. The estimated slope is 1.4. The sum of residuals is 0 3.2 5 38
Simple Linear regression 1. A researcher uses a simple linear regression to measure the relationship between the monthly salary (Salary measured in dollars) of data scientists and the number of years since being awarded a Master degree (Master Degree). A random sample of 80 observations was collected for the analysis. A researcher used the econometric model which has the following specification Salary,-β0 + β, Master-Degree, + εί, where i = 1, , 80 The (incomplete) Excel output of equation (1)...
19. (2pts) Which of the following is NOT an assumption in simple linear regression? o The &i's have variance o2. o The Ɛi's are normally distributed. o The response variable y is normally distributed for each value of x. O The εi's are linearly related to x. 20. (2pts) The Central Limit Theorem states that the sampling distribution of X1 – X2 is (approximately) normal: o When at least one of the sample sizes is greater than or equal to...
Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer.i) The OLS Sample regression equation passes through the point of sample means ii) The sum of the estimated () equals the sum of the observed ; or the sample mean of the estimated () equals the sample mean of the observed .iii) The OLS residuals (i = 1, …, N) are uncorrelated with...
In a simple linear regression analysis, the following sum of squares are produced: ∑(y−y¯)2=500 ∑(y−y′)2=100 ∑(y′−y¯)2=400 The proportion of the variation in Y that is explained by the variation in X is: a.) 80% b.) 20% c.) 50% d.) 25%
Part A Consider the Simple Linear Regression model. If the COV[X,Y] = 2.4, VAR[X] = 1.2, X-bar = 9.6, and Y-bar = 23.4, then compute the slope coefficient Beta1. Provide your answer with three decimal places of precision, e.g. 0.001. Part B Consider the Simple Linear Regression model. If the COV[X,Y] = 2.4, VAR[X] = 1.2, X-bar = 9.6, and Y-bar = 23.4, then compute the intercept Beta0. Provide your answer with three decimal places of precision, e.g. 0.001.
step by step please ? ? QUESTION 04 (20 points) - Simple Linear Regression (SLR) We have the following hypothetical data for the independent variable x (other names: regressor, covariate, or explanatory variable) and the dependent variable y (regressand). Obs. х y x² ху 1 8.34 0.75 ? ? 2 3.21 2.37 10.30410 3 5.96 3.80 ? 1.27 4.40 ? 5.58800 5 4.28 2.52 ? TOTAL ? ? ? (a) Use Excel to draw a y-x scatter diagram with y...