The table below represents the values of discharge and stage. Extend the rating curve for these data, using the following equations [q= k(g-a), k= 10A, a-0]. Try to estimate the values of k and b by least square method. Determine the value of discharge at stage 7m. Stage (m) 4. Discharge (m'/s) 50 20 10
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- Determine the best (according to sum-of-squares-measure) curve y = Aebx, through the dataabove.Transformed equationln(y) = ln(A) + bxorY = a + bx.the least squares regression line for predicting the temperature from the chirp rate is y=32.298+12.297x. If the two chirp rates differ by 1.5 chirps per second, by how much would the temperature differ?A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is y = 1.4 + 0.97 x. For a student with a right and left hand span of 24 cm, what is the value of the residual? Give your answer to 2 decimal places.
- A regression analysis between weight (y in pounds) and height (x in inches) resulted in following least squares line: y^= 120+5x. this implies that if the height is increased by 1 inch, the weight is expected ?Battery life has a strong, negative, linear relationship with temperature. If the least-squares regredsion line using x = temperature explains 90% of the variation in battery life, what is the correlation, r, between battery life and temperature.The number of inches that a recently built structure sits on the ground is given by (image) where x is its age in months. Use the least squares method to estimate alpha.
- A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.69 + 0.1656 length. A newborn was 48cm long and weighed 33kg. According to the regression model, what was his residual? What does that say about him?The common cricket can be used as a crude thermometer. The colder the temperature, the slower the rate of chirping. The table below shows the average chirp rate of a cricket at various temperatures. The least squares regression line for predicting the temperature from the chirp rate is y=32.298+12.297x. If two chirp rates differ by 1.5 chirps per second, by how much would the temperature differ?A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent. Predict the number of days absent for an employee that lives 5 miles from the hospital.
- A college bookstore must order books two months before each semester starts. They believe that the number of books that will ultimately be sold for any particular course is related to the number of students registered for the course when the books are ordered. They would like to develop a bestfitting line to predict how many books to order. From past records, the bookstore obtains the number of students registered, X, and the number of books actually sold for a course, Y , for 12 different semesters.A scatterplot of the data along with the best fitting line is presented below. a. The correlation between the two variables is r = .89. Calculate and interpret the value of r2.b. The equation for the best fitting line is Y = 9.30 + 0.673X. Explain and interpret the value of 9.30.c. How many books should the store order for a class of 50 students? Would you trust this prediction?In a study, researchers are investigating the link between the distance a person lives from a grocery store (the explanatory variable, in miles) and their life expectancy (the response variable, in years). From their data, they calculate a least squares regression line y^ = 79.6 - 0.3x What is the predicted life expectancy for a person who lives 4.1 miles away from a grocery store, according to this equation? Round your answer to 2 decimal places. Please show work!!A regression analysis was applied between the sales data (in $1000s) and advertising data (in $100s) and the fitted regression line obtained is Y=1.2x+18. If advertising is $2000, what is the point estimate for the sales?