Question

Table 2 below presents the output for sample data relating the number of study hours spent by students outside of class during a three week period for a course in Business Statistics and their score in an examination given at the end of that period.

Table :2

SUMMARY OUTPUT Regression Statistics Multiple R 0.862108943 R Square 0.74323183 Adjusted R Square 0.700437135 Standard Error 6.157605036 Observations 8 ANOVA df SS MS F Significance F Regression 1 658.5034 658.5034 17.36738 0.005895 Residual 6 227.4966 37.9161 Total 7 886 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 40.08163265 8.889551 4.508848 0.004065 18.32969 61.83358 18.32969 61.83358 X Variable 1 1.496598639 0.359119 4.167419 0.005895 0.617867 2.375331 0.617867 2.375331

1. Determine the least-square regression line for the data.
2. Give an interpretation of the fitted slope, β.
3. Based on R² value, assess the strength of the linear relationship between study hour and examination grade.
4. Using the above output, determine whether sufficient statistical evidence exists to conclude that there is a positive linear relationship between study hour and examination grade at the 5% level of significance.

Answer 1

a.

The least-square regression line for the data is,

= 40.08163265 + 1.496598639 X

b.

The score in an exmination is predicted to be increased by 1.496598639 when the number of study hours spent by students outside of class for a course in Business Statistics increases by 1 hour.

c.

R2 = 0.74323183

Since the R2 value is close is near 0.75, there is a significant strength of the linear relationship between study hour and examination grade.

d.

Test statistic, t = 4.508848

Degree of freedom = df Residual = 6

P-value = P(t > 4.508848, df = 6) = 0.002

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and thus there exists sufficient statistical evidence to conclude that there is a positive linear relationship between study hour and exmination grade at the 5% level of significance.