Question

The following table contains data from 16 former elementary statistics students, where x represents the number of absences a student had for the semester and y represents the student’s final class average.

Absences	Class Average
2	86
2	83
3	81
10	53
3	92
7	71
9	68
1	79
12	53
9	78
1	77
1	85
13	62
1	97
10	54
3	79

(a) Draw a scatter plot using one the following website(s): http://www.alcula.com/calculators/statistics/scatter-plot/ or https://www.meta-chart.com/scatter
(b) Estimate the correlation in words (positive, negative, or no correlation)
(c) Calculate the correlation coefficient, r.
(d) Determine whether r is statistically significant at the 0.01 level of significance.
(e) Determine whether r is statistically significant at the 0.05 level of significance.
(f) Calculate the coefficient of determination, r2.
(g) Interpret the meaning of r2 for the given set of data.
(h) Find the equation of the least-squares regression line, if appropriate.

Answer 1

a) scatter plot

b)Correlation coefficient r=-0.8453 is strong negative correlation

c) Correlation coefficient r = -0.8453

d)a significance level of 0.01 indicates a 1% risk of concluding that a difference exists when there is no actual difference.

e)The researcher determines the significance level before conducting the experiment. The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

f) coefficient of determination R^2 = 0.714503

g)R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

here coefficient of determination =0.71 is indicates that the model explains the 0.71 % variability of the response data

h) Regrassion equation Y = 89.11166199612 - 2.6182366889416 * X

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.845283
R Square	0.714503
Adjusted R Square	0.69411
Standard Error	7.531747
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1987.569	1987.569	35.03731	3.74E-05
Residual	14	794.1811	56.72722
Total	15	2781.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	89.11166	3.05454	29.17351	6.13E-14	82.56033	95.663	82.56033	95.663
X Variable 1	-2.61824	0.442327	-5.91923	3.74E-05	-3.56693	-1.66954	-3.56693	-1.66954