The table shown below gives six pairs of x and y values. y 16 8 20 13 12 10 4 6 9. 4 Using the regression of y on x, the predicted value of y for x = 17, rounded to two decimal places, is:
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- The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.Which of the following best describes a regression coefficient in a bivariate setting? a. The change in Y predicted by a unit change in X b. The slope of a line that minimizes the sum of squared residuals c. The correlation coefficient multiplied by SDy/SDx d. All of the aboveAn article reported that for a regression of y = average SAT score on x = expenditure per pupil, based on data from n = 44 New Jersey school districts, a = 766, b = 0.015, r2 = 0.160, and se = 53.7. One observation in the sample was (9400, 897). What average SAT score would you predict for this district, and what is the corresponding residual?Predict average SAT score _______ Residual ________
- A linear regression model has been estimated for the variables Y="monthly consumption of veal (kg)", X1="monthly monetary household income (thousand EUR)" and X2="household size (number of members)" using data for a random sample of 80 households. The following results have been obtained: b0=0.3 b1=0.5 b2=0.7 R-sq=0.9 R=0.95，Interpret the value of regression coefficient b2.A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90, R2 = 0.67; DW = 2.08 How would you interpret the above ‘Output’ of a regression analysis performed in SPSS?We want to estimate the effect of x on y using a simple linear regression. Assume that the MLR 1-6 hold and the true effect of x is zero. What is the probability that the t-statistic of the slope coefficient in the above regression is positive? a. 5% b. +/- 1.96 c. 95% d. 50%
- A. Identify the regression analyses necessary for testing this initial model. B. What are the direct and indirect effects of z2 on z5?Suppose we run a regression of Y on X using the following data points( xy)in a sample: (0, 1,(1,2).(-10, 9). What is the OLS regression line and what is the RSS? A:1+2X, RSS=3 B:1+X, RSS=0 C:2+X, RSS=-1 D:2+X, RSS=0A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = -20; SSx = 4; My = 7; Mx = 3 What is b equal to? What is a equal to? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
- Using data on class size(CS) and average test scores(TS) from 150 middle school classes, estimates the OLS regression, TS_hat = 750 -5.5(CS), R^2=0.7 . The sample average class size for the 150 classes is 20. What is the sampel average test score for the 150 classes?A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.586 Stdev width: 0.877 Mean height: 13.037 Stdev height: 1.697 Correlation coefficient: 0.7814 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.X Y 5 10 3 6 6 7 4 3 2 4 a. Compute the Pearson correlation. b. Find the regression equation for predicting Y from X. c. Calculate SSresidual