Use Equations (3.5) and (3.6) to estimate the coefficients of the line y = ax + b such that the sum of the squared deviations between the line and the following data points is minimized. a. x 1.0 2.3 3.7 4.2 6.1 7.0 y 3.6 3.0 3.2 5.1 5.3 6.8
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- Determine the best (according to sum-of-squares-measure) curve y = Aebx , through the data above. Transformed equation ln(y) = ln(A) + bx or Y = a + bx.Carrie and Ryan have both computed the slope of the least-squares line using data for which the standard deviation of the x-values and the standard deviation of the y-values are equal. Carrie gets a value of 0.5 for the slope, and Ryan gets a value of 2. One of them is right. Which one?Two types of feed have been developed for a freshwater fish raised in fish farms. 40 of the fish fed with the first feed and 50 of the fish fed with the second feed were randomly selected and average weight gains were found to be 175 gr and 130 gr, respectively. Which of the following is the point estimate of the difference in average weight gain of fish fed two feeds?
- The least-squares regression equation is y=728.0x+14,705 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8165. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is ___%, on average. For a median income of $0, the percent of adults with a bachelor's degree is ____%.Determine the best (according to sum-of-squares-measure) curve y = Axb, through the data above. Transformed equation ln(y) = ln(A) + b ln(x) or Y = a + bX.Determine the best (according to sum-of-squares-measure) curve y = Aebx, through the dataabove.Transformed equationln(y) = ln(A) + bxorY = a + bx.
- A value of r close to _______ suggests at most a weak linear relationship between the variables.Q9: Assume that a researcher wants to estimate the proportion of “A” grade scorers in STAT101 course for the population of SEU students in 2020. Assume also that the proportion of “A” grade scorers in 2020 is not known. How many SEU students must be surveyed from STAT101 course in order to be 90% confident and the margin of error should not exceed two percentage points? (Given zα/2 = 1.64). 1- 1821 2- 1781 3- 1618 4- 1681(A) The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to? (B)An outbreak of certain illness was attributed to ice creams produced at a certain factory. Scientists measured the level of the illness causing factor in 10 randomly sampled batches of ice cream. The levels were: 0.583, 0.242, 0.129, 0.691, 0.231, 0.693, 0.619, 0.392, 0.418. What is the estimated interval of population mean at 0.05 level of significance? (C) The population standard deviation for the age of a certain University students is 13 years. If we want to be 90% confident that the sample mean age is within 3 years of the true population mean age of the University students, then how many randomly selected students must be surveyed?
- The equation of the line containing the points (−2,−4) and (2,5) is y=2.25x+0.5. Compute the sum of the squared residuals of the given data set for this line. The sum of the squared residuals for the line containing the points (−2,−4) and (2,5) isA regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat in the cereal gave the following results: Calories = 97.1053 + 9.6525*(grams of fat). Which of the following is FALSE: It is estimated that for every additional gram of fat in the cereal, the number of calories increases by about 9. It is estimated that in cereals with no fat, the total amount of calories is about 97. If a cereal has 2 g of fat, then it is estimated that the total number of calories is about 113. If a cereal has about 145 calories, then this equation indicates that it has about 5 grams of fat. One cereal has 140 calories and 5 g of fat. Its residual is about 5 cal.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?