For the following data points X 1 2 4 y 1 4 a. find the linear interpolation spline b. find the quadratic interpolation spline? 3. 2. 3.
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A: Explanation of the answer is as follows
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4For the following data (0, 22), (15, 24), (18, 37), (22, 25), (24, 123) what three data points of x should you choose for quadratic interpolation to find y(14.9)?Determine the best (according to sum-of-squares-measure) curve y = ax + b, through thedata below.
- Suppose that weights of college mathematics textbooks in the United States are normally distributed with mean µ = 2.25 lbs and variance σ2 = 0.2025 lbs. Find the weight that corresponds to Q3 and interpret this measure of position in the context of the problem.The following data is given:x 0 2 3 5 6y 1 1 7 11 20Question 1 Determine the best (according to sum-of-squares-measure) curve y = ax + b, through the data above.If the value of D40 is 82, therefore, ____ of the data is less than or equal to 82.
- Each of 25 teenage girls with one brother was asked to provide her own height (y), in inches, and the height (x), in inches, of her brother. The scatterplot below displays the results. Only 22 of the 25 pairs are distinguishable because some of the (x,y) pairs were the same. The equation of the least-squares regression line is ŷ = 35.1 + 0.427x.*Girls are on the y-axis and brothers are on the x-axis* a.) Draw the least-squares regression line on the scatterplot above. b.) One brother’s height was x = 67 inches and his sister’s height was y = 61 inches. Circle the point on the scatterplot above that represents this pair and draw the segment on the scatterplot that corresponds to the residual for it. Give a numerical for the residual. c.) Suppose the point x = 84 , y = 71 is added to the data set. Would the slope of the least squares regression line increase, decrease, or remain about the same?Explain. Would the correlation increase, decrease, or remain about the same? Explain.The director of a local Tourism Authority would like to know whether a family’s annual expenditure on recreation (y), measured in $000s, is related to their annual income (x), also measured in $000s. In order to explore this potential relationship, the variables x and y were recorded for 10 randomly selected families that visited the area last year. The results were as follows: Week 1 2 3 4 5 6 7 8 9 10 x 41.2 50.1 52.0 62.0 44.5 37.7 73.5 37.5 56.7 65.2 y 2.4 2.7 2.8 8.0 3.1 2.1 12.1 2.0 3.9 8.9 The summary statistics for these data are: Sum of x data: 520.4 Sum of the squares of x data: 28431.42 Sum of y data: 48 Sum of the squares of y data: 343.74 Sum of the products of x and y data: 2858.63 (i) Draw a scatter diagram of these data.The director of a local Tourism Authority would like to know whether a family’s annual expenditure on recreation (y), measured in $000s, is related to their annual income (x), also measured in $000s. In order to explore this potential relationship, the variables x and y were recorded for 10 randomly selected families that visited the area last year. The results were as follows: Week 1 2 3 4 5 6 7 8 9 10 x 41.2 50.1 52.0 62.0 44.5 37.7 73.5 37.5 56.7 65.2 y 2.4 2.7 2.8 8.0 3.1 2.1 12.1 2.0 3.9 8.9 The summary statistics for these data are: Sum of x data: 520.4 Sum of the squares of x data: 28431.42 Sum of y data: 48 Sum of the squares of y data: 343.74 Sum of the products of x and y data: 2858.63 Calculate the sample correlation coefficient. Interpret the findings.