A researcher collected data from a small random sample of tenstudents by asking them individually how much time (y) they spentstudying and how much time (x) they spent on social media, on oneday during an exam week. Both times were given in hours, rounded tothe nearest half hour. They shown in the table below.
| x | 5 | 2.5 | 3 | 4.5 | 2.5 | 2 | 3 | 2 | 6.5 | 6 |
| y | 2 | 4.5 | 2 | 1 | 4 | 3.5 | 2 | 4 | 0 | 0.5 |
The researcher wishes to find a simple linear regression modelYi ? N(a + bxi , ?2 ).
(i) Find data summaries for this data and use them to calculateestimates for the slope and intercept parameters (b and a) for thislinear regression. (ii) Construct the ANOVA table for thisregression. (iii) Calculate the coefficient of Determination, R2and comment on how well the regression line fits the data. (iv)Find a 90% confidence interval for the mean expected number ofhours of studying in a day, for an individual who spends 1.5 hourson social media.
