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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Respiratory 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.
- A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.3 14.9x Coefficients (Intercept) X Estimate St 4.3 Ho: B₁ = 0 Ha: B₁ > 0 B1 O Ho: B₁ Ha: B₁ <0 = 0 14.9 B1 O Ho: B₁ = 0 0 Ha: B1 Std. Error Test statistic P-value 2.9 5.1 1.48 Specify the null and the alternative hypotheses that you would use in order to test whether a negative linear relationship exists between x and y. 2.92 0.08 0.01A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 3.3 +12.7x Coefficients (Intercept) X Estimate Std. Error Test statistic O Ho: B₁: = 0 Ha: B₁ 0 O Ho: B₁ = 0 Ha: B₁ 0 12.7 2.2 6.4 1.5 1.98 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a positive linear relationship exists between x and y. 0.08 0.03Class Activity 5 Q4. Considering the following two distributions, which statement is correct? a) SD of the distribution A is larger than that of distribution B. b) Mode of the distribution A is larger than that of distribution B. c) Range of the distribution A is smaller than that of distribution B. d) Mean of the distribution A is larger than that of distribution B. e) A data item with z-score of -1 falls between 30 to 40 in distribution A. f) A data item with z-score of +1 falls between 10 to 20 in distribution B. A B 10 20 30 40 50 60 70 80 90 100
- A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 03. (a). Differentiate the different types of linear regression and describe the use of regression in geographical study. (b). Calculate the value of the slope, b, for observations of n = 22, r2 = 0.73, standard deviation of x = 2.3 and the regression sum of square = 1324.The slope of a regression line (y on x) is -0.24, we know that SDy=3.2 and SDx=4.0, then the correlation coefficient between the two variables is:A. 0.3B. -0.3C. 0.8D. -0.8
- B b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between a = average number of passing yar and y = the percentage of games won by the team. c. Develop the estimated regression equation that could be used to predict the percentage of games won given the avera passing yards per attempt. Enter negative value as negative number. WinPct =| |)(Yds/Att) (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 1 decimal). The slope of the estimated regression line is approximately So, for every increase : of one yar number of passes per attempt, the percentage of games won by the team increases by %. e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was was 5.5. Use th regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs.…The regression equation for for the association between BMI and total cholesterol level is: y = 28.07 + 6.49x A.) Suppose a participant has a BMI of 26. What would we estimate the total cholesterol to be? B.) Suppose two individuals have a mean BMI that differs by 3 units. What is the estimated difference in total cholesterol. C.) What ranges of BMI should the equation be used to predict total cholesterol?10) A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-0.767 b=31.009 r2=0.609961 r=-0.781 Use this to predict the number of situps a person who watches 7.5 hours of TV can do (to one decimal place)