Given the bivariate data: 3 5 2 3 2 1 5 Y 6 (a) Fit a regression line of Y on X and thence predict Y if X = 5. (b) Fit a regression line of X on Y and thence predict X if Y = 2.5 (c) Calculate Karl Pearson's coefficient.
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- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?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.
- The birth lengths in cm (x) and birth weights in kg (y) of a sample of 50 newborn female babies are compared, yielding a correlation coefficient of r=0.578 and a linear regression equation of ŷ =−8.89+0.243x The babies all had lengths between 46.5 and 53.0 cm, and weights between 2.50 and 4.05 kg. Based on this, predict the birth weight of a newborn female baby with a birth length of 48.5 cm.The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433x7. in a regression model involving 44 observations, the following estimated regression equation was obtained. Y =29+18 X1 +43 X2 +87 X3 For this model SSR = 600 and SSE = 400 . The critical value of F for testing the significance of the above model at 5% level is A. 2.61 B. 0.67 C. 2.84 D. None E. 8.59
- Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n observations on x and y, you estimate the model by OLS and obtain the estimates βˆ 0, βˆ 1, and the R-squared of the regression, R2 . Then you scale this sample by a factor of 100, obtain a new sample {xi/100; yi/100} for i = 1, . . . , n, re-estimate the model by OLS, and denote the new coefficient estimates by β˜ 0, β˜ 1, and the new R-squared of the regression by R˜2 . a) Give the expression of β˜ 1 in terms of βˆ 1, and justify your answer.The 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 multiple coefficient of determination is _____.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.
- You conduct a regression of the squared residuals against the dummy variables X1, X2, and X3 and find that for the squared residuals regression: Multiple R 0.4145 R Square 0.1718 Adjusted R Square 0.1600 SEE 92.3760 Conduct a test at the level to see if conditional heteroskedasticity is present In view of your answer for a), what needs to be done?A regression equation is given by y = 11.37395 + 2.82773x. The following informantion about the variable x and y is also given. Calculate the value of xyA multiple linear regression model based on a sample of 13 weeks is developed to predict standby hours based on the total staff present and remote hours. The SSR is 23,638.17 and the SSE is 33,273.99. c. Compute the coefficient of multiple determination, r2, and interpret its meaning. (Round to four decimal places as needed.)