An article reports on the determination of silver content of galena crystals gro

Question

An article reports on the determination of silver content of galena crystals grown in a clased hydrothermal system over a range of ternperature. Crystallization temperature in Celcius crystal i, the incindert variable, and Ag2S (Ag25) in tnolecule % is the dependent variable; we wish to mKKlel AF2S from crystallization. The following summary statistics are calculated for you and a scatterplot is also provided. (No R portion since I am providing it and you are to only interpret what you find, not run the analysis) cryatal-c (398,292,352,575,568,450,50,408,484,350,503,600,600) Ag2S c.15,.05..23,.43,.23,.4. .44..44..45..09..59..63..6) plot (crystal,Ag2S,main- 'Rau data Scatterplot' Raw data Scatterplot 300 400 500 600 crystal summary (silver) silver-1n (Ag2S-crystal); Call: la(formula Ag2S -cryatal) Residuals: Q Median 30 -0.27200 -0.08203 0.03736 0.06831 .18109 Coefficients Estimate Std. Error t value Pr(>It!) (Intercept) -0.3114957 0.1736832 -1.793 0.10040 0.0014322 0.0003602 3.976 0.00217 signif, codes : 0 . ‘ 0.001 .** . 0.01 .*. 0.05 0.1 . . 1 Residual standard error: 0.1306 on 11 dogreen of freedon Multiple R-squared: 0.5897, Adjusted R-squared: 0.5524 F-atatistic: 15.81 on 1 and 11 DF, p-value: 0.002174 eTh.' Incorporation of Uraiam and Silver by Hydro hermal y Synchoind Gakna" (Koumowuic Gnoagy, 19610r3-1024). (a) State the model equation and state what each component of the model is (b) List assumptions of regression (ether with mathematical kymbols or in words) (e) Find the equation of the regression line (aso called the Least Squares Regression Line). That is, find the values of Ap and and put it in the form =+ 'z. Even though the output is provided, calculate (by hand using the provided summary statistics) the intercept (o and theslope (). (d) Using your regrewoon equation, estimate the silver content when temperature is 503C (find when x=503). (e) Based on your calculation in part b, calculate the residual. What does it mean (did we overestimate or underestimate the silver content)? The observed value of silver content for a temperature of 53 is 0.59. (0 What is the correlation r and what does it mean What is the value of R and what does it meRn (R) Is the slope significant? Using the provided output, conduct a test to decide whether there is a linear association between crystallization temperature and silver content. List hypotheses, test statistic, pvue results, and conclusion in context. (h) Based on your answers d and e, what is your ment of this modelt Good, bad? A correct answer will make references to the conclusions in parts () and () AgaS Menn 71.538 104.69 0.7679 SD 0.195 Min 292 Max 600 0.63

Explanation / Answer

a)
The model equation is formed using the coefficients as

Silver = -0.3114 + 0.00143*crystal

the components are
intercept = -0.3114
and crystal = 0.00143
b)
Assumption #1: Your two variables should be measured at the continuous level
Assumption #2: There needs to be a linear relationship between the two variables.
Assumption #3: There should be no significant outliers.
Assumption #4: You should have independence of observations,
Assumption #5: Your data needs to show homoscedasticity,
Assumption #6: Finally, you need to check that the residuals (errors) of the regression line are approximately normally distributed

c)
The equation of the regressionline

Silver = -0.3114 + 0.00143*crystal
where b0 = -0.3114
and b1 = 0.00143

d)
put the value of crystal temp at 500 c
in the regression equation as
Silver = -0.3114 + 0.00143*500 = 0.4036

Please note that we can answer onyl 4 subparts of a question at a time , as per the answering guidelines

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