In summer it seems that fewer students appear to attend clas

In summer, it seems that fewer students appear to attend class on afternoons when the weather is warm then when it is cold outside. To test this theory, you collect data regarding outside temperature and attendance from 10 randomly selected lecture classes for several randomly selected days during the academic year. Summary statistics of the data are provided below:

Solution

Let X be temperature and Y be attendance.

We have to find correlation coefficient between X and Y.

We are given that,

Xbar = 69

Ybar = 70

SSx = 842

SSy = 912

SSxy = -787

The formula is,

r = SSxy / sqrt[ SSx*SSy ]

r = -787 / sqrt (842*912)

r = -787 / 876.3013

r = -0.8981

The fitted linear model is

Y = a + b*X

where a = Ybar - b*Xbar

b = SSxy / SSx = -787 / 842 = -0.9347

a = 70 - (-0.9347*69) = 134.4929

The fitted linear model is,

Y = 134.4929 - 0.9347*X

The total variation is explained by the fitted linear model is R² (square of the correlation coefficient)

R² = -0.8981² = 0.8066 = 80.66%

It expresses the proportion of the variation in Y which is explained by variation in X.

Let X : Determinants of a cognitive test score(DSST)

Y : Vitamin D level.

correlation coefficient is -0.811. it indicates that there is negative relationship between X and Y

Here we are given that 95% CI, (-1.081, -0.541)

That is population parameter is lie in this interval.