X Y 8 8 4 6 4 7 Find the regression equation for predicting Y from X. Σχ SSx ΣΥ ΣΧΥ SP 6. 3. 3. 2. 2. 1.
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- XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.
- A linear regression line y = 80 + 0.2x is computed to predict the final exam score y on the basis of the first score x on the first test. Suppose Maria scores a 95 on the first test. What would be the predicted value of her score on the final exam? STEP 1: Substitute the value of the first test into the equation of the linear regression line. y = 80 + 0.2 STEP 2: Solve the equation of the linear regression line.y =The regression model Yi=−303.8+1.5949X1i−0.0699X2i predicts standby hours based on total staff present, X1i, and remote hours, X2i, for week i. The data from which the model was constructed are provided. b. If appropriate, perform the Durbin-Watson test, using α=0.05. Determine the Durbin-Watson statistic.Suppose that a regression relationship is given by the following:Y = β0 + β1X1 + β2X2 + εIf the simple linear regression of Y on X1 is estimated from a sample of n observations, the resulting slope estimate is generally biased for β1. However, in the special case where the sample correlation between X1 and X2 is 0, this will not be so. In fact, in that case the same estimate results whether or not X2 is included in the regression equation.a. Explain verbally why this statement is true.b. Show algebraically that this statement is true.
- If the regression constant is 9.1410114235and the regression coefficient is 0.90613879. Present the data in a textual manner. Just presentation; no need for calculation please. Note: A college faculty collected data on his students’ general weighted average (Y) in the first semester and their high schoolaverage grade (X).A linear multiple regression model is given as: Y = βo + β1 X1 + β2 X2 + μ a. Determine the parameters of this model b. Explain the circumstance under which X1 be called an endogenous variable?A fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y = 9, the residual at this observation is:
- he following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384. The yearly income of a 24-year-old female individual isThe regression equation is calculated to be y' = 5.333 + 0.777x. After conducting a hypothesis test, your decision is to fail to reject the null hypothesis. Predict the value of y' when x=11. A researcher wants to determine if the number of years of education for a parent correlates with the number of years of education for their child. The table shows the number of years of education of the parent and the number of years of education of their child for a random sample of 7. Years of Education of Parent 13 9 12 10 12 10 12 Years of Education of their Child 15 11 10 16 17 12 17 The regression equation is calculated to be y' = 5.333 + 0.777x. After conducting a hypothesis test, your decision is to fail to reject the null hypothesis. Predict the value of y' when x=11. 5.333 13 14 13.88In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation as ˆ y = 14 + 0.5 x y ^ = 14 + 0.5 x where y is the final-exam score and x is the score on the first test. Andrea scored 75 on the first test. What is the predicted value of the Andrea's score on the final exam? Andrea scored 56.5 on the final exam. What is the value of the residual?
