d) Construct a 95% prediction interval about the value of y if x = 4. Lower Bound Jpper Bound Round to one decimal place as needed.)
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- A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, xx, and the weight in tens of pounds, yy. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years is given by 1.272±0.5701.272±0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval? A)We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds. B)We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear’s weight of between 7.0 and 18.4 pounds. C)We are 95 percent confident that for every one-year increase in the age of black bears in the sample,…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 2A multiple regression includes two regressors: Yi = b0 + b1X1i +b2X2i + ui. What is the expected change in Y if X1 increases by 8 unitsand X2 is unchanged? What is the expected change in Y if X2 decreasesby 3 units and X1 is unchanged? What is the expected change in Y if X1increases by 4 units and X2 decreases by 7 units?
- (d) Determine the equation of the regression line using least squares method.(e) What is the expected breakdown for an eleven year old machine?what is a confidence coefficinent for a simple linear regression line whoes alpha =0.05 and line is y(hat)=-7.45-10xGiven the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?
- A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that b1=1.4379 and Sb1=0.1397. a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal? b. Construct a 95% confidence interval estimate of the population slope, β1. a. Determine the hypotheses for the test. Choose the correct answer below. A. H0: β1=0 H1: β1≠0 B. H0: β0≤0 H1: β0>0 C. H0: β1≤0 H1: β1>0 D. H0: β0≥0 H1: β0<0 E. H0: β1≥0 H1: β1<0 F. H0: β0=0 H1: β0≠0 Compute the test statistic. The test statistic is ? (Round to two decimal places as needed.) Determine the critical value(s). The critical value(s) is(are) ? (Use a comma to separate answers as needed.…The fish in my pond have mean length 12.53 inches with a standard deviation of 2.37 inches and mean weight 4.83 pounds with a standard deviation of .4 pounds. The correlation coefficient of length and weight is .3. If the length of a particular randomly selected fish is reported to be 17 inches, and if we use simple linear regression to predict the weight of a fish whose length is reported to be 15.8 inches long, then what is the expected squared error?For variables x1, x2, x3 and y satisfying the assumptions for multiple linear regression inferences, the population regression equation is y = 27 – 4.7x1 + 2.3x2 + 5.8 x3. For samples of size 20 and given values of the predictor variables, the distribution of the estimates of β1 for all possible sample regression planes is a _________ distribution with mean _________ and standard deviation _______.
- What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places.Imagine that you first estimate an OLS regression with a random sample of 100 observations and then re-estimate the same regression with 100 additional observations which are also randomly sampled. What would you expect to happen as the sample size increases? a. 95 percent confidence intervals get narrower b. R-squared increases c. Standard errors increase d. Sum of squared residuals decreases