QUESTION 1 The amount of steam used (kg/m3) per month (Y) at a plant is thought to be dependent on the average monthly ambient temperature (X) in degrees Fahrenheit (F). The past years usage and temperature are as follow: Temperature (OF) Usage per month (kg/m3) 21 180 24 215 32 283 47 422 50 434 59 549 68 620 74 665 62 552 50 482 41 370 30 272 i) State the dependent and independent variables. ii) Write the regression equation for the data by finding the value of slope (b) and constant (a). Interpret the slope of the regression line in the context of this problem. iii) Find the correlation coefficient and interpret the value obtained. iv) Calculate the coefficient of determination and explain its meaning. v) Estimate the number of kilograms of steam used per month if the average monthly ambient temperature is 70 F.QUESTION 2 A newly designed highway sign is being examined. A test on the sign visibility distance is to be conducted. Thus, twelve drivers, of various ages, are tested to see at what maximum distance (in meter) each driver could clearly read the sign. Each driver's age and the sign visibility distance are recorded in the following table. Age 18 22 23 32 37 46 53 67 68 70 73 Distance 155 170 140 124 128 137 140 124 91 118 85 109 The Minitab output for the above data is as follows. Regression Analysis: Distance (m) versus Ages Predictor Coef SE Coat Constant 169.16 11 . 10 15.24 0.000 Ages -0. 8611 0 . 2064 -4.17 0.002 S = 15.4649 R-Sg = ? R-Sq(adi) = 59.98 Analysis of Variance Source DF SS MS P Regression 1 4162.6 4162.6 17. 40 0.002 Residual Error 10 2391.6 239.2 Total 11 6554.3 ) Based on the data given, find the correlation coefficient and explain its meaning. i) What is the name of the statistics that mark with "?', find and explain its meaning? iii) Write the linear regression equation. iv) Estimate the average distance at which a sign can be read by a 33-year-old driver. v) Perform a test at 5% significance level to determine whether the linear regression model is significant.QUESTION 3 As a new type of environmentally friendly natural air freshener is being developed, it is tested to see if the length of time that the air freshener lasts (in days) is affected by the temperature. The data collected was analyzed and the output is shown below. Temperature (C) Length of time that the air freshener lasts (in days) BL 24 20 22 24 21 38 15 33 18 32 19 36 17 Regression Analysis: Length of time versus Temperature (C) Analysis of Variance Source SS MS Regression 55.230 55.2304 Error 2. 484 0. 4968 Total 57. 714 Model Summary S = 0. 704826 R-Sq = Y R-Sq (adj ) = 94.84% Coefficients Predictor Coef SE Coef T F Constant 30, 36 1. 07 28.37 0.000 Temperature ("C) -0. 3805 0. 0361 -10.54 0.000 ) State the dependent and independent variables. i) Write down the equation of line that describes the relationship between the independent and dependent variables. iii) Determine the correlation coefficient iv) What is the name of the statistic mark with 'Y', find the value and interpret its meaning v) Test whether the linear regression model is significant or not. Use a = 0.05. vi) Estimate the length of time that the air freshener lasts if the temperature is 30"C