Question

An experiment was carried out to study the effect of a certain medication to decrease heart rate in adults. The independent variable is the dose in milligrams of the medication, and the dependent variable is the difference between the lowest heart rate after administration of the medication and a control before administration. egin{tabular}{|c|c|} hline Data (mg) ( mathrm{x} ) & Decrease in heart rate (beats/min) ( mathrm{y} ) \ hline 0.5 & 10 \ hline 0.75 & 8 \ hline 1 & 12 \ hline 1.25 & 12 \ hline 1.5 & 14 \ hline 1.75 & 12 \ hline 2 & 16 \ hline 2.25 & 18 \ hline 2.5 & 17 \ hline 2.75 & 20 \ hline 3 & 18 \ hline 3.25 & 20 \ hline 3.5 & 21 \ hline end{tabular} a. Establish the null and alternative hypotheses. b. Perform the calculations manually to find the equation of simple linear regression. c. Find the coefficient of determination. d. Use the square root equation to find the coefficient of correlation. e. Prove the null hypothesis that ( eta=0 ) using a level of significance of 0.05 . f. Determine the p-value for each hypothesis test. g. Obtain the ( 95 % ) confidence interval for ( eta ).

          An experiment was carried out to study the effect of a certain medication to decrease heart rate in adults. The independent variable is the dose in milligrams of the medication, and the dependent variable is the difference between the lowest heart rate after administration of the medication and a control before administration.
egin{tabular}{|c|c|}
hline Data (mg) ( mathrm{x} ) & Decrease in heart rate (beats/min) ( mathrm{y} ) \
hline 0.5 & 10 \
hline 0.75 & 8 \
hline 1 & 12 \
hline 1.25 & 12 \
hline 1.5 & 14 \
hline 1.75 & 12 \
hline 2 & 16 \
hline 2.25 & 18 \
hline 2.5 & 17 \
hline 2.75 & 20 \
hline 3 & 18 \
hline 3.25 & 20 \
hline 3.5 & 21 \
hline
end{tabular}
a. Establish the null and alternative hypotheses.
b. Perform the calculations manually to find the equation of simple linear regression.
c. Find the coefficient of determination.
d. Use the square root equation to find the coefficient of correlation.
e. Prove the null hypothesis that ( eta=0 ) using a level of significance of 0.05 .
f. Determine the p-value for each hypothesis test.
g. Obtain the ( 95 % ) confidence interval for ( eta ).

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An experiment was carried out to study the effect of a certain medication to decrease heart rate in adults. The independent variable is the dose in milligrams of the medication, and the dependent variable is the difference between the lowest heart rate after administration of the medication and a control before administration.
egintabular|c|c|
hline Data (mg) ( mathrmx ) Decrease in heart rate (beats/min) ( mathrmy ) hline 0.5 10 hline 0.75 8 hline 1 12 hline 1.25 12 hline 1.5 14 hline 1.75 12 hline 2 16 hline 2.25 18 hline 2.5 17 hline 2.75 20 hline 3 18 hline 3.25 20 hline 3.5 21 hline
endtabular
a. Establish the null and alternative hypotheses.
b. Perform the calculations manually to find the equation of simple linear regression.
c. Find the coefficient of determination.
d. Use the square root equation to find the coefficient of correlation.
e. Prove the null hypothesis that ( eta=0 ) using a level of significance of 0.05 .
f. Determine the p-value for each hypothesis test.
g. Obtain the ( 95 % ) confidence interval for ( eta ).

Added by Stephen C.

Instant Answer

Solved by Expert Sheryl Ezze

10/18/2023

Step 1

The null hypothesis (H0) is that there is no relationship between the dose of the medication and the decrease in heart rate, i.e., the slope of the regression line (β) is zero. The alternative hypothesis (H1) is that there is a relationship between the dose of the Show more…

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Transcript

00:01 So we want to determine whether there's a linear association between this data the number of milligrams of a certain drug that's to decrease the heart rate and we want to see if there's a linear relationship so we're gonna assume that beta is zero or that there is no linear relationship and alternately that beta does not equal zero now we can do it as a two -tailed test or a one -tailed test that it's a positive association that the more drugs you use the more it will decrease the heart rate but let's just find it conservatively whether there's a linear now.

00:33 It says perform the calculations to find the equation of and let me click go to your manually to find the equation of the simple regression so if you're going to do this manually you would find the correlation coefficient first and then you would show that these and you know, it goes through the x bar y bar point and you know that you find the slope by taking the correlation coefficient times the standard deviation y over the standard deviation of x and then you can find what the y intercept is by taking and plugging into your into your model and i'm not going to go through and show that show all this with the time constraints that i have here but we know that it goes through so we have that y bar is equal to a plus and we would have just calculated the slope and you plug in the x bar.

01:27 And so your a coefficient will equal the y bar minus the slope that you calculate times the x bar so you can get that model so i'm going to use my software and go to stat tests and i'm going to go to a linreg t -test and i find that that model comes out to be seven point zero five five and then plus four point zero eight eight times x now part b part c.

02:02 I'm sorry part c says to find the core core the coefficient of determination well, the coefficient of determination is that our squared value and is point nine zero three eight six and then part d says use the square root of the equation to find the coefficient of the correlation...

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