Chapter 10, Problem 10.82CRP

An environmentalist monitored the water quality of a river in city Xby measuring the conductivity of the river monthly. The conductivity of a water body is an early indicator of the water quality. Owing to implementation of activities which were harmful to the nature such as an oil spill, the conductivity in µS/cm of the river decreased. However, a continuous cleaning up plan had been carried out for the river from January until April 2020 and the conductivity measurement for the months had improved as follows:   a1, a2, a3, a4, a5…, an 3, 12, 27, 48, 75, …., an   1. Let an represents the conductivity for nmonths since January 2020. By using n in the formula, determine the formula to represent the conductivity sequence, an. 2.What is the estimated conductivity for January 2021? 3. By assuming bn-1= an - an-1, the monthly improvement of conductivity can be represented by the following sequence. Based on the given sequence, determine bn. b1, b2, b3, b4, …, bn = (12-3), (27-12), (48-27),…

For a MR model with 4 predictors, we have: SSE 288 and SST = 957 What percentage of the variation in Y is accounted for by its assumed relationship with the predictors?

I’m interested in assessing whether someone’s resting heart rate (X) is related to how fast they are able to finish running a 5k race (5k is 3.1 miles) (Y). I gather data from a set of runners and want to see whether, at an alpha of 0.05, there is a significant relationship between resting heart rate and finish time. Use the data below to answer this question: Resting Heart Rate (measured in beats/min) Finish Time (measured in minutes) (Y) 54 30 65 33 60 35 60 32 75 35 70 36 80 45 60 36 55 29 55 27 60 30 please write the equation for the line of best fit for this data (use the form: y’ predicted = b(slope)X + a (intercept)   What is the R2 value? What does it represent in this problem’s context?

I’m interested in assessing whether someone’s resting heart rate (X) is related to how fast they are able to finish running a 5k race (5k is 3.1 miles) (Y). I gather data from a set of runners and want to see whether, at an alpha of 0.05, there is a significant relationship between resting heart rate and finish time. Use the data below to answer this question: Resting Heart Rate (measured in beats/min) Finish Time (measured in minutes) (Y) 54 30 65 33 60 35 60 32 75 35 70 36 80 45 60 36 55 29 55 27 60 30 What are the degrees of freedom for this problem? What is the critical R value?  ______________________________________________________________   Calculate the sum of squares for X ________________________   Calculate the sum of squares for Y ________________________

Twelve workers at a production line were asked to take a special three-day intensive course to improve their productivity. At the beginning and again at the end of the course, they were given a particular task to see the improvement in their productivity. Based on the data recorded for the two variables Number of years of experience X and Improvement (number of units per minute) Y, the following sums were calculated.   xi = 96,      yi = 132, xi2 = 892,   yi2 =1510, xiyi= 1110     Consider estimating a simple linear regression model of the form   y = b1 + b2x + e   Q2. Sample mean of X, X, is   96 12 8 11   Q3. Sample Variance of Y, SY2, is   5.72 11.27 5.27 4.91   Q4. Sample correlation between X and Y, Corr(X, Y), is   0.46 0.50 0.64 -0.64

Data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 46 wines, a model was created using the percentages of aloohol to predict wine quality Y-0.337 +0.5635X,, where X, in the alcohol content (%) and Y, is the rated quality of the wine. For these data, Syx 0.9316, X 10.63, and h 0.027260 when X 10. Complete parta (a) throi a. Construct a 05% confidence interval estimate of the mean wine quality rating for all wines that have 10% alcohol. 4.988 spypx= 10 s 5.608 (Type integers or decimals. Round to three decimal places as needed. Use ascending order) b. Construct a 95% prediction interval of the wine quality rating of an individual wine that has 10% alcohol. (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)

A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) 0.5 -0.5 0 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 9 4 4 5 8 13 14 17 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 6.512 + 5.472 BMI change 20 S 5.26270 R-Sq 27.16% R-Sq (adj) 19.88% 15- : 10- -0.5 0.0 1.5 Ⓡ S 5.26270 Coefficients Term Coef VIF SE Coef 2.26 T-Value 2.88 P-Value 0.0164 Constant 6.512 BMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change = 6.512 + 5.472 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to…

Special dyes have been developed that only bind to DNA. The intensity of the color is directly related to the quantity of DNA present in the cell. A haploid cell would have a “low” amount of color, a cell in G1 would have a “medium” amount of color, and a cell in M phase would have a “high” amount of color.   Is this sort of assessment quantitative, qualitative or semi-quantitative? Justify your reasoning.

14. s = t² – sec t + 1 -