A sad fact of getting older is that some skills start to decline. Let’s examine the extent to which age can be used to predict motor skill. Load data set motor_skill (provided with this assignment).

Due: Tuesday, 05/08, at 2:00 PM, in my mailbox, which is on the 8th Floor of the Humanities Building on the West side of the floor (coming off the elevators, the Psychology side of the floor is to the left). The psychology department mailboxes are above the copy machine.​​

Format: Students may: (a) Print out A08 and write answers directly on it, or (b) Type answers to A08 directly on it and then print it out.; either way, please make sure that your assignments are legible and easy to follow. Students who submit messy and/or poorly organized assignments often lose points. When submitting paper assignments, please staple any work with multiple pages.

A sad fact of getting older is that some skills start to decline. Let’s examine the extent to which age can be used to predict motor skill. Load data set motor_skill (provided with this assignment). This contains data from 210 participants recruited for an online study. Each participant reported their age and then completed a test of motor skill. Motor skill scores are expressed as a percentage, from 0 (worst score possible) to 1 (best score possible).

-1- Using the Scatterplots tab in ESCI, create a scatterplot of the relationship between age and motor skill. Does this data seem suitable for use with regression?

-2- To what extent is age and motor skill related in this sample (i.e., what is the correlation between age and motor skill)? What is the 95% CI for the relationship between age and motor skill in the general population?

-3- What is the regression equation for predicting motor skill from age (Hint: In ESCI’s Scatterplots tab make sure to check Red 9 to reveal the regression panel)?

-4- A second study was conducted with 13 participants recruited from the same online service. For each participant, use the Scatterplots tab in ESCI to predict motor skill from age. Record the prediction and the 95% prediction interval.

-a- In the table above, how often was the real motor skill within the prediction interval? Does this mean that this data set gives amazing predictive powers? Why or why not?

-b- For each prediction, calculate the residual and fill in the residual column of the table above.

-c- No math, just think: If you were to average the residuals, what do you expect to find? (Hint: Remember that you sometimes over-estimate a true score and you sometimes underestimate a true score)

-d- What is the actual average of residuals that you found? Is it close to 0 as you expected?

-e- Because residuals tend to average out, we need a better way of tracking how wrong our predictions are. The last column in the above table is labeled Residual2. Square each residual so that only positive values remain, sum them all up, then average, then take the square root. What is the value that you obtain? Does age seem like a particularly strong predictor of motor skill?