If the omitted variable is negatively correlated with the treatment (x1,x2)<0 and has a positive impact on the outcome(b2>0), then the effect of b1 is overestimated or underestimated?
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- Similarly show that the F-statistic for the interaction is the square of the t-statistic for the contrast САВ = (H11 – H12 – H21 + l22)/2 - Explain why this contrast is the correct one to use in order to examine the presence of an interaction.Imagine you would like to estimate the following model Bo B₁cigarettes_day + u health = where health is self-rated health on a 1 to 5 scale (5 = very healthy) and cigarettes_day is the number of cigarettes the person smokes per day (on average). Imagine you would like to estimate B₁ using an instrumental variable (IV) regression. As instrument, you would use the variable female, which is equal to 1 if the person is female and 0 otherwise. For the situation described above, a) state the IV relevance assumption b) state the IV exogeneity assumption In your answer, use the actual variable names (instead of e.g. x, y and z).Suppose we conduct a study on the time spent studying for an exam and exam scores. We survey students in introductory statistics and find the explanatory variable (time, in hours) ranges from 0 to 16 and exam scores (in points, out of 100 maximum) range from 5 to 100. The correlation between time spent studying and exam scores is 0.80. We fit a simple linear regression model to these data and get the following least squares line: score = 4 + 6*(time). You pick a random student from the course and observe that the number of hours she studied for the exam is 1 standard deviation above the mean time spent studying. How many standard deviations above or below the mean exam score would you expect her to score?
- There is no significant difference between the perceived level of riskiness of thrill behavior in males and in females. (Use α= 0.05) There is no significant difference between the perceived level of riskiness of rebellious behavior in males and in females. (Use α= 0.10) There is no significant difference between the level of riskiness of thrill-seeking items and rebellious items as perceived by the males. (Use α= 0.05).You run a regression analysis on a bivariate set of data (n=32). With ¯x=22.4 and y¯=65.8, you obtain the regression equation y=−3.812x+52.761 with a correlation coefficient of r=−0.137 You want to predict what value (on average) for the response variable will be obtained from a value of 70 as the explanatory variable.What is the predicted response value? y = (Report answer accurate to one decimal place.)A team of social workers wants to compare the different effects of treatments for complex trauma. They divide 21 clients into 3 groups (n=7 each) that donot differ significantly from one another in terms of pretreatment trauma. one group gets (TFCBT), one group gets (EGT) and one receives a combination of the two (TF+EG). Clients symptoms are evaluated after treatment using a clinician interview where scores from range from 0-30 and higher scores indicate a higher severity. What test should be ran to see if there is a difference in post-treatment scores among the three treatments, and what graph should I use?
- Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the regression analysis with all three predictor variables?You have two (hypothesis) tests with the same significance level α = 0.05 but their powerfunctions are different; the power function of test A is higher than the power function of testB. Which test is your choice? Justify your answer.The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2
- A scientific foundation wanted to evaluate the relation between y= salary of researcher (in thousands of dollars), x1= number of years of experience, x2= an index of publication quality, x3=sex (M=1, F=0) and x4= an index of success in obtaining grant support. A sample of 35 randomly selected researchers was used to fit the multiple regression model. Parts of the computer output appear below. Based from the table, what is the constant term of the multiple linear regression?Researchers are studying pomegranate’s antioxidant properties to see if it might have any beneficial effects in the treatment of cancer. One such study investigated whether pomegranate fruit extract (PFE) was effective in slowing the growth of prostate cancer tumors. In this study, 24 mice were injected with cancer cells, then the mice were randomly assigned to one of three treatment groups. The data on y = average tumor volume (in mm3) and x = number of days after injection of cancer cells for the mice that received plain drinking water is shown in picture below: a. Find (to three decimal places) zy, and zxzy for the pair (23,580): zy = zxzy = b. Compute Pearson’s sample correlation coefficient for the given data to four decimal places. c. Compute the slope, b, for the least-squares regression line to two decimal places d. Use b to calculate a and write the equation for the least-squares regression line a= y= e. Predict the average tumor volume (y) for a mouse 20 days…A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) Depression Score Change S = The accompanying computer output is from Minitab. Depression score change 15- 10- -0.5 S Fitted Line Plot Depression score change = 6.577 +5.440 BMI change 20- 5.30586 Coefficients T 0.0 0.5 -0.5 R-sq 25.96% - 1 Term Coef Constant 6.577 BMI change 5.440 % 0.5 BMI change 1.0 SE Coef 2.28 2.90 9 0 0.1 0.7 0.8 1 1.5 4 T-Value 2.88 1.87 Interpret this estimate. s is the typical amount by which the ---Select--- line. 4 5 Regression Equation Depression score change = 6.577 +5.440 BMI change P-Value 0.0164 0.0906 S 5.30586 25.96% R-Sq R-Sq (adj) 18.56% 8 (b) Give a point estimate of o. (Round your answer to…
