Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0
Q: Given the data as shown in the table below X Y 56 0.86 44 0.93 68 0.85 76 0.87 94 0.73
A: Consider the given dataset: X Y 56 0.86 44 0.93 68 0.85 76 0.87 94 0.73
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Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint
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- A paper† gave 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. JMP output for these data is shown below. A scatterplot titled "Bivariate Fit of Depression Score Schange by BMI Change" has 12 points and a line plotted on it. The horizontal axis is labeled "BMI change" and ranges from about −0.8 to about 1.8. The vertical axis is labeled "Depression score change" and ranges from about −2 to 20. The points are plotted from left to right in an upward, diagonal direction starting from the middle left of the diagram. The points are very scattered and are between approximately −0.5 to 1.5 on the horizontal axis and between approximately −1 to 18 on the vertical axis. A line with positive slope titled "Linear Fit" is drawn across the plot to approximate the trend of the points. The line enters the viewing window at about (−0.8, 3) and exits at…Select True or False for each statement, depending on whether the corresponding statement is true or false. 1. Multicollinearity is a situation in which two or more independent variables are highly correlated with each other. 2. In a multiple regression problem, the regression equation is y^=60.6−5.2x1+0.75x2. The estimated value for y when x1=3 and x2=4 is 48. 3. In a multiple regression problem involving 24 observations and three independent variables, the estimated regression equation is y^=72+3.2x1+1.5x2−x3. For this model, SST=800 and SSE=245. The value of the FF statistic for testing the significance of this model is 15.102. 4. For each x term in the multiple regression equation, the corresponding β is referred to as a partial regression coefficient.find the minimum for the upper quartile
- In an analysis of a sample of bivariate data concerning the soil acidity x (in pH) and germination time y (in days) for tomato seeds, a linear regression model is constructed and follows the equation y^=−1.22x+5y^=−1.22x+5 Select the most appropriate statement about the linear correlation exhibited. A. The data set exhibits strong positive linear correlation. B.We cannot determine anything about the strength or direction of linear correlation from this information alone. C. The data set exhibits strong negative linear correlation. D. The linear correlation coefficient is -1.22.Q4 / The probability of the percentage of salts not matching the sand from a particular source is 0.2, and the probability of its grained gradient not matching the specifications is 0.03, so the probability of the sand matching the specifications is equal?For 50 randomly selected speed dates, attractiveness ratings by males for their female date partners (x) are recorded along with the attractiveness ratings by females of the male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yeild x=6.3, y=6.0, r= -0.163, p value= 0.259, and y ( with the ^) above it = 7.27 - 0.208x. Find the best predicted value of Y (attractiveness rating by female of male) for a date in which the attractiveness rating by male of the female is x=6. Use a 0.05 significance level. The best predicted value of Y when x=6 is ??
- Researches are interested in whether or not the average fuel economy for compact cars is thesame as sedan cars. A sample of 36 compact cars and 25 sedan cars is taken.The sample of compacts returns a mean of ̄X = 38 miles per gallon and sample variance of s^2 = 25.The sample of sedans returns a sample mean ̄Y = 36 with a sample variance of s^2 = 49.Let μ 1 be the population mean of compacts and μ 2 for sedans. a. Create a 95% confidence interval for μ 1 .b. Now create a 95% confidence interval for μ 1 μ 2 .c. Say the interval from part b. contains 0. What can you say about the difference in the averagefuel economy of compact cars versus economy carsA researcher found a linear correlation between course grades and the average number of hours spent on a mobile phone each day. The line of best fit has equation y ^ = 3.7 − 0.786 x with correlation coefficient r = − 0.84. a. Does this prove that spending too much time on a phone causes students to get lower grades? b. What does the regression line predict your final grade in a course will be if you spend an average of 150 minutes per day on your phone?For the linear regression model Y = bo + b1(X): The p-value for the intercept is large: about 0.98 The p-value for the slope is very small: less than 2 times 10^(-16) What can we conclude? Since the p-value for the intercept is large, we can conclude that there is not a strong correlation between X and Y. Since the p-value for the intercept is large, we can conclude that there is a very strong correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very weak correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very strong correlation between X and Y. We are not able to assess the strength of the correlation between X and Y with the output provided.
- Suppose you obtain the following regression model, E[y]=20+53*x +33*x^2. What is the impact of a 63 unit change of x on the expected value of y when x is at its mean of 54?6. Suppose you walk a hiking trail at a speed which is uniformly distributed from 4 to 6 miles per hour. The distance of the trail is 24 miles. Find the PDF of the duration of the trip. (Note: speed = distance/time)
