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###### Please do Q1 before attempting this question. You can make useof the standard error from Q1, and the R command qt(prob,df) Thisgives the value such that the area to the left of this value undera t-distribution curve with df degrees of freedom is equal to prob.Alternatively, you can obtain the multiplier needed using thestatistical tables. The margin of error for a 99%confidence interval for the slope of the regression line in thepopulation is?Q1 data below-Question 1Embryonic stem cells have the

Please do Q1 before attempting this question. You can make use of the standard error from Q1, and the R command qt(prob,df) This gives the value such that the area to the left of this value under a t-distribution curve with df degrees of freedom is equal to prob. Alternatively, you can obtain the multiplier needed using the statistical tables. The margin of error for a 99% confidence interval for the slope of the regression line in the population is? Q1 data below- Question 1 Embryonic stem cells have the capacity to produce neural progenitor cells, providing a potential means of repopulating cells lost due to spinal cord injury. However cell survival using existing methods is often low. Aiming to improve this, researchers investigated growing cells inside fibrin scaffolds and looked at the effect of two growth factors, neurotrophin-3 (NT3) and a platelet-derived growth factor (PDGF), on the outcomes. Mouse embryonic stem cells were cultured in 16 wells seeded with fibrin scaffolds to which various concentrations of the growth factors (in ng/mL) were added. With at least 5000 cells in each well, fluorescence-activated cell sorting was used after three days to count the number of living and dead cells in each well. The data from the 16 wells are presented below. The Alive variable gives the proportion of the cells alive after three days. PDGF,NT3,Cells,Alive 0,0,7520,0.479 0,0,8970,0.553 0,10,8310,0.632 0,10,7430,0.603 0,20,6930,0.500 0,20,8030,0.604 0,30,8520,0.812 0,30,7130,0.877 2,0,7720,0.655 2,0,7680,0.580 2,10,7500,0.681 2,10,8280,0.549 2,20,7740,0.746 2,20,7960,0.708 2,30,8620,0.817 2,30,7330,0.708 Please read the data into R as seen in previous lab sessions (see R-Summary.pdf for details) and call the resulting data frame welldata. We would now like to determine the P-value to test for an assocation between the proportion of cells alive and NT3 concentration. This is equivalent to testing whether or not the slope of a regression is zero (a two-sided hypothesis test). You would get the same p-value if you try to predict Alive from NT3 or NT3 from Alive. Here, the NT3 concentration can be measured immediately and in practice we would have to wait to measure the proportion of cells Alive. Hence it makes more sense to use Alive as the response (Y) variable and NT3 as the explanatory (X) variable. We will ignore the other variables in this analysis. You should work out the required test statistic using relevant formulae, your calculator and some R commands. You can then determine the corresponding p-value using R. Note that if you had to determine the p-value for a slope using tables, you would get a range, rather than a single answer. You can run a linear regression using NT3 as the X variable and Alive as the Y variable via the following R command. We will store the results in a structure called reg, which we then take a brief look at by just typing its name. Please use the commands as follows. Note that lm, which stands for linear model, is an R function which can be used to fit a linear regression to data. reg <- lm(Alive ~ NT3,welldata) reg The above only shows you the estimates of the intercept and slope, i.e. b0 and b1. Please make a note of these for Q2. However, there is a lot more information stored in reg. You can work out the standard deviation of the residuals (using the n-2 degrees of freedom) via the following R command, in which you need to enter n yourself: sqrt(sum(reg$residual^2)/(n-2)) You can work out the bottom line of the s.e.(b1) formula using the following R command: sqrt( sum( (welldata$NT3- mean(welldata$NT3))^2 ) ) You then have all the information needed to work out the standard error of the slope estimate (b1). Make a note of this for use with Q3. You can then work out the required p-value by making use of the following command, which gives the area to the left of a value t under a t-distribution curve with df degrees of freedom: pt(t,df)