In a study of copper bars, the relationship between shear stress in ksi (x) and shear strain in % (y) was summarized by the least-squares line y = – 20.00 + 2.56x. There were a total of n = 17 observations, and the coefficient of determination was r2 = 0.9111. If the total sum of squares was
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardA study was conducted to assess the relationship between students’s score in final exam (y) and number of hours spent for exam (x) in each day. Data on a random sample 20 students were obtained and a regression model was estimated; and the least squares estimates obtained are: intercept a=28.5 and slope b=4.3 with SE(b)=Sb=0.017. The SS are: TSS=2540 and ESS=850. ****** QA) What is the difference between exam score obtained by two students one who studied 5 hours and the other who studied 9 hours per day. QB) In the above Question 1, find 95% CI for the slope and interpret it. In the above Question 1, find and interpret the coefficient of determination (r-square value).arrow_forward
- The sum of squares error (SSE) for the above data is;arrow_forwardIn multiple regression analysis involving 10 independent variables and 100 observations, the critical value tt for testing individual coefficients in the model will have:A. 10 degrees of freedomB. 89 degrees of freedomC. 100 degrees of freedomD. 9 degrees of freedom In a multiple regression analysis involving 40 observations and 5 independent variables, the total variation SST=350 and SSE=50. The multiple coefficient of determination is:A. 0.8469B. 0.8529C. 0.8408D. 0.8571arrow_forwardA regression model involving 8 independent variables for a sample of 69 observations resulted in the following sum of squares. SSE = 306 SST = 1800 Compute the multiple coefficient of determination. At 5% of level of significance, test to determine whether or not the model is significant. Question 3: A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 Write out the estimated regression equation for the relationship between the variables. Compute coefficient of determination. Can you interpret the strength of the…arrow_forward
- Q3. Find out the regression coefficients of Y on X and of x on Y on the basis of following data: Ex = 50, X = 5, EY = 60, Y = 6, EXY = 350 Variance of X= 4, Variance of Y= 9arrow_forwardA professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. A) Find the regression equation for predicting GPA from SAT scores. B) What percentage of the variance in GPAs is accounted for by the regression equation (i.e., compute the correlation, r, then find r2)? C) Does the regression equation account for a significant portion of the variance in GPA? Use a = .05 to evaluate the F-ratio.arrow_forwardA simple regression model developed for ten pairs of data resulted in a sum of squares of error, SSE = 125. The standard error of the estimate is 12.5 3.5 25 15.6 O 3.95arrow_forward
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