The following data represents the amount in kg of fertilizer applied to equal size of plots and the yields in kg of maize.PLOTAMOUNT OF FERTILIZER(X)YIELDS(Y)A27B13C38D410 (a) Calculate and interpret the correlation coefficient for X and Y (b) Calculate and interpret the least square regression of Y on X

Given information: Correlation(X, Y)=0.9648

Answered: The following data represents the…

The following data represents the amount in kg of fertilizer applied to equal size of plots and the yields in kg of maize. PLOT AMOUNT OF FERTILIZER(X) YIELDS(Y) A 2 7 B 1 3 C 3 8 D 4 10

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Interpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.
A market study found that the sales for a firm were related to advertising expenditure, as follows: Advertising Expenditure (Kshs ‘000’) Sales (Kshs ‘000’) 0 13 1 16 2 14 3 22 4 17 5 21 6 26 Required Draw a scatter diagram with the line of best fit to show the relationship. Determine the regression line equation for estimating the sales for a given level of advertising expenditure What is the estimated sale in thousand, if no advertising expenditure is incurred?
What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Coefficient Std Error т P Constant -2298.36 158.531 -14.50 0.0000 Size 11598.9 230.111 50.41 0.0000 Resid. Mean Square (MSE) R-Squared Adjusted R-Squared 0.8925 1248950 0.8922 Standard Deviation 1117.56 Interpret the coefficient of determination for the regression model. A) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. C) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha =…
Find the equation for the least squares regression line of the data described below. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. Round your answers to the nearest thousandth. y = L Submit
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The authors of the paper "Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickness, Egg Surface Area of Japanese Quails Using Various Egg Traits as Regressors"t used a multiple regression model with two independent variables where y = quail egg weight (g), X, = egg width (mm), and X2 = egg length (mm). The regression function suggested in the paper is -21.658 + 0.828x, 0.373x2. + (a) What is the mean egg weight for quail eggs that have a width of 20 mm and a length of 48 mm? (Enter your answer to three decimal places.) (b) Interpret the value of B,. O When width is fixed, the mean increase in weight associated with a 1-mm increase in length is 0.373 g. When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.373 g. O When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.828 g. O When width is fixed, the mean increase in weight associated with a 1-mm increase…
Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars). X₁ = display floor space (square meters), X₂= competitors' advertising expenditures (thousands of dollars), X₁ = advertised price (dollars per unit). Predictor Intercept FloorSpace CompetingAds Price Coefficient 1,243.88 13.74 -6.848 -0.1461 (a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) *FloorSpace+ *CompetingAds+ (b-1) The coefficient of FloorSpace says that each additional square foot of floor space O takes away 13.74 from sales (in thousands of dollars) O adds about 13.74 to sales (in thousands of dollars) adds about 6.848 to sales (in thousands of dollars) takes away 01496 from sales (in thousands of dollars) (b-2) The coefficient of CompetingAds…
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The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.972. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y= - 0.0070x + 44.4405. Complete parts (a) and (b) below. Click the icon to view the data table. ..... (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. Data Table (Round to one decimal p Full data set gas mileage Miles per Weight (pounds), x Weight (pounds), x Miles per Gallon, y Car Car Gallon, y…