Question

Grades and Social Media ~ A college student wants to find out whether there is a relationship between time spent in minutes on social media platforms per day throughout the semester and the end of term percentage grade. The student collects a random sample of 20 students and records the time spent in minutes and the end of term percentage grades.
Minutes spent on social media is the X variable and End of term percentage grade is the Y variable in this scenario.

R output Coefficients:              Estimate       Std. Error     t value        Pr(>|t|)     (Intercept)    103.884        2.8426        36.545        < 2e-16 *** Minutesspent   -0.1683        0.0213        -7.635         4.73e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 4.89 on 18 degrees of freedom Multiple R-squared: 0.7641, Adjusted R-squared: 0.751 F-statistic: 58.3 on 1 and 18 DF, p-value: 4.732e-07

What is the lower bound for a 90% confidence interval for the true slope β1β1 of the regression line? Give your answer to 4 decimal places.

Answer 1

Given that ,

df = 18

Critical value = 1.330

Lower bound = -0.1683 - 1.330 * 0.0213 = -0.1966